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Fission rates and transactinide formation in the r-process. Igor Panov. Subject of the talk. Fission in the R-process Astrophysical site for the main r-process Actinides and transactinides Data: T 1/2 , P n , (n,g), (n,f), b df, s.f. Renovation of data for the r-process: - PowerPoint PPT Presentation
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Fission rates and transactinide formation in
the r-process
Igor Panov
Subject of the talkSubject of the talk
bull Fission in the R-process bull Astrophysical site for the main r-processbull Actinides and transactinidesbull Data T12 Pn (ng) (nf) df sf bull Renovation of data for the r-process Purpose and motivation bull Pdf different approaches ndash S
bull samples of predictionsbull conclusions
bull Seeger Fowler Clayton 1965 Seeger Fowler Clayton 1965 fission -fission - long and short solutionslong and short solutionsbull TThielemahielemannn n Me Mettzzingeingerr K Klapdor lapdor ZZttPPhhyys A309s A309 (1983) 301(1983) 301 P Pdfdf
bull Lyutostansky Panov Ljashuk Izv RAN ser fiz 1990 PLyutostansky Panov Ljashuk Izv RAN ser fiz 1990 Pdfdf
bull PMoller JRNix K-LKratzPMoller JRNix K-LKratz ADNDT 66 (1997) 131 ADNDT 66 (1997) 131 TT1212 P Pinin
bull Goriely et al Goriely et al Astron Astrophys 346 798ndash804 (1999)Astron Astrophys 346 798ndash804 (1999) sfsfbull Panov et al Nucl Phys A 718 (2003) 647 Panov et al Nucl Phys A 718 (2003) 647 (nfission) vs P(nfission) vs Pdf df
bull IKorneev et al NIC-2006 Astronomy Letters 66 (2008) 131 IKorneev et al NIC-2006 Astronomy Letters 66 (2008) 131 YYffff(ZA)(ZA)bull KKelic elic et al et al PPhhysys L Leetttt B B 616 616 (2005) (2005) 48 48 YYffff(ZA)(ZA)bull IV Panov E Kolbe F-K Thielemann T Rauscher B Pfeiffer K-L Kratz IV Panov E Kolbe F-K Thielemann T Rauscher B Pfeiffer K-L Kratz
NP A 747 (2005) 633 NP A 747 (2005) 633 (nfission) (n(nfission) (n) P) Pdf df
bull GMartinec-Pinedo et al Progress in Particle and Nuclear Physics 59 (2007) GMartinec-Pinedo et al Progress in Particle and Nuclear Physics 59 (2007) 199 199 (nfission) vs P(nfission) vs Pdf df
bull Y-Z Qian Y-Z Qian Astron JAstron J 569 (2002) p L103 569 (2002) p L103 Kolbe Langanke FullerKolbe Langanke Fuller Phys Phys
Rev Lett 2004Rev Lett 2004 induced fissioninduced fissionbull I Petermann et al NIC-2008 GMartinec-Pinedo et al GMartinec-Pinedo et al ProgrProgr in in Particle Particle
and Nucland Nucl Phys Phys 5959 ((20072007)) 199-205 199-205 (nfission) P(nfission) Pdf df sfsf induced finduced fbull K Langanke G Martinez-Pinedo IPetermann FK Thielemann PPNP 2011
(nfission) P(nfission) Pdf df sfsf induced finduced f
Importance of fission for the r-processImportance of fission for the r-process
fission
Main r-process R ge05 s cycling number ncycl (log2(YfinYinit)) gt 0 ~1
Model of Model of NSM-simulation Freiburghaus et al AJ 525 (1999)
Y(A) during r-process with fission cycling for NSM conditions Y(A) during r-process with fission cycling for NSM conditions (t-duration time of the r-process t=0 - initial composition)(t-duration time of the r-process t=0 - initial composition)
Panov I Thielemann F-K Astronomy Letters Vol 30 (2004) 711
11 -delayed rates-delayed rates - - Pdf for Zlt100
22 (n(n)-rates )-rates Zlt115Zlt115
33 Neutron-induced fission rates Neutron-induced fission rates nifnif ~ lt ~ lt vgt vgt Zlt115
44 Spontaneous fission Spontaneous fission ndash phenomenologicalndash phenomenological models Zlt115 models Zlt115
55 -decay -decay Zlt115Zlt115
66 Mass predictions ETFSI HFB Thomas-Fermi Zlt115Mass predictions ETFSI HFB Thomas-Fermi Zlt115
77 ConclusionsConclusions
motivation further data reevaluation in the actinide and transactinide region
Bf lt Sn nuclei with Bf ge Sn inclined crosses nuclei with neutron binding energy predicted by the ETFSI [5] Sn sim 2 MeV and dots nuclei in which 2 gt Sn gt 0
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Subject of the talkSubject of the talk
bull Fission in the R-process bull Astrophysical site for the main r-processbull Actinides and transactinidesbull Data T12 Pn (ng) (nf) df sf bull Renovation of data for the r-process Purpose and motivation bull Pdf different approaches ndash S
bull samples of predictionsbull conclusions
bull Seeger Fowler Clayton 1965 Seeger Fowler Clayton 1965 fission -fission - long and short solutionslong and short solutionsbull TThielemahielemannn n Me Mettzzingeingerr K Klapdor lapdor ZZttPPhhyys A309s A309 (1983) 301(1983) 301 P Pdfdf
bull Lyutostansky Panov Ljashuk Izv RAN ser fiz 1990 PLyutostansky Panov Ljashuk Izv RAN ser fiz 1990 Pdfdf
bull PMoller JRNix K-LKratzPMoller JRNix K-LKratz ADNDT 66 (1997) 131 ADNDT 66 (1997) 131 TT1212 P Pinin
bull Goriely et al Goriely et al Astron Astrophys 346 798ndash804 (1999)Astron Astrophys 346 798ndash804 (1999) sfsfbull Panov et al Nucl Phys A 718 (2003) 647 Panov et al Nucl Phys A 718 (2003) 647 (nfission) vs P(nfission) vs Pdf df
bull IKorneev et al NIC-2006 Astronomy Letters 66 (2008) 131 IKorneev et al NIC-2006 Astronomy Letters 66 (2008) 131 YYffff(ZA)(ZA)bull KKelic elic et al et al PPhhysys L Leetttt B B 616 616 (2005) (2005) 48 48 YYffff(ZA)(ZA)bull IV Panov E Kolbe F-K Thielemann T Rauscher B Pfeiffer K-L Kratz IV Panov E Kolbe F-K Thielemann T Rauscher B Pfeiffer K-L Kratz
NP A 747 (2005) 633 NP A 747 (2005) 633 (nfission) (n(nfission) (n) P) Pdf df
bull GMartinec-Pinedo et al Progress in Particle and Nuclear Physics 59 (2007) GMartinec-Pinedo et al Progress in Particle and Nuclear Physics 59 (2007) 199 199 (nfission) vs P(nfission) vs Pdf df
bull Y-Z Qian Y-Z Qian Astron JAstron J 569 (2002) p L103 569 (2002) p L103 Kolbe Langanke FullerKolbe Langanke Fuller Phys Phys
Rev Lett 2004Rev Lett 2004 induced fissioninduced fissionbull I Petermann et al NIC-2008 GMartinec-Pinedo et al GMartinec-Pinedo et al ProgrProgr in in Particle Particle
and Nucland Nucl Phys Phys 5959 ((20072007)) 199-205 199-205 (nfission) P(nfission) Pdf df sfsf induced finduced fbull K Langanke G Martinez-Pinedo IPetermann FK Thielemann PPNP 2011
(nfission) P(nfission) Pdf df sfsf induced finduced f
Importance of fission for the r-processImportance of fission for the r-process
fission
Main r-process R ge05 s cycling number ncycl (log2(YfinYinit)) gt 0 ~1
Model of Model of NSM-simulation Freiburghaus et al AJ 525 (1999)
Y(A) during r-process with fission cycling for NSM conditions Y(A) during r-process with fission cycling for NSM conditions (t-duration time of the r-process t=0 - initial composition)(t-duration time of the r-process t=0 - initial composition)
Panov I Thielemann F-K Astronomy Letters Vol 30 (2004) 711
11 -delayed rates-delayed rates - - Pdf for Zlt100
22 (n(n)-rates )-rates Zlt115Zlt115
33 Neutron-induced fission rates Neutron-induced fission rates nifnif ~ lt ~ lt vgt vgt Zlt115
44 Spontaneous fission Spontaneous fission ndash phenomenologicalndash phenomenological models Zlt115 models Zlt115
55 -decay -decay Zlt115Zlt115
66 Mass predictions ETFSI HFB Thomas-Fermi Zlt115Mass predictions ETFSI HFB Thomas-Fermi Zlt115
77 ConclusionsConclusions
motivation further data reevaluation in the actinide and transactinide region
Bf lt Sn nuclei with Bf ge Sn inclined crosses nuclei with neutron binding energy predicted by the ETFSI [5] Sn sim 2 MeV and dots nuclei in which 2 gt Sn gt 0
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
bull Seeger Fowler Clayton 1965 Seeger Fowler Clayton 1965 fission -fission - long and short solutionslong and short solutionsbull TThielemahielemannn n Me Mettzzingeingerr K Klapdor lapdor ZZttPPhhyys A309s A309 (1983) 301(1983) 301 P Pdfdf
bull Lyutostansky Panov Ljashuk Izv RAN ser fiz 1990 PLyutostansky Panov Ljashuk Izv RAN ser fiz 1990 Pdfdf
bull PMoller JRNix K-LKratzPMoller JRNix K-LKratz ADNDT 66 (1997) 131 ADNDT 66 (1997) 131 TT1212 P Pinin
bull Goriely et al Goriely et al Astron Astrophys 346 798ndash804 (1999)Astron Astrophys 346 798ndash804 (1999) sfsfbull Panov et al Nucl Phys A 718 (2003) 647 Panov et al Nucl Phys A 718 (2003) 647 (nfission) vs P(nfission) vs Pdf df
bull IKorneev et al NIC-2006 Astronomy Letters 66 (2008) 131 IKorneev et al NIC-2006 Astronomy Letters 66 (2008) 131 YYffff(ZA)(ZA)bull KKelic elic et al et al PPhhysys L Leetttt B B 616 616 (2005) (2005) 48 48 YYffff(ZA)(ZA)bull IV Panov E Kolbe F-K Thielemann T Rauscher B Pfeiffer K-L Kratz IV Panov E Kolbe F-K Thielemann T Rauscher B Pfeiffer K-L Kratz
NP A 747 (2005) 633 NP A 747 (2005) 633 (nfission) (n(nfission) (n) P) Pdf df
bull GMartinec-Pinedo et al Progress in Particle and Nuclear Physics 59 (2007) GMartinec-Pinedo et al Progress in Particle and Nuclear Physics 59 (2007) 199 199 (nfission) vs P(nfission) vs Pdf df
bull Y-Z Qian Y-Z Qian Astron JAstron J 569 (2002) p L103 569 (2002) p L103 Kolbe Langanke FullerKolbe Langanke Fuller Phys Phys
Rev Lett 2004Rev Lett 2004 induced fissioninduced fissionbull I Petermann et al NIC-2008 GMartinec-Pinedo et al GMartinec-Pinedo et al ProgrProgr in in Particle Particle
and Nucland Nucl Phys Phys 5959 ((20072007)) 199-205 199-205 (nfission) P(nfission) Pdf df sfsf induced finduced fbull K Langanke G Martinez-Pinedo IPetermann FK Thielemann PPNP 2011
(nfission) P(nfission) Pdf df sfsf induced finduced f
Importance of fission for the r-processImportance of fission for the r-process
fission
Main r-process R ge05 s cycling number ncycl (log2(YfinYinit)) gt 0 ~1
Model of Model of NSM-simulation Freiburghaus et al AJ 525 (1999)
Y(A) during r-process with fission cycling for NSM conditions Y(A) during r-process with fission cycling for NSM conditions (t-duration time of the r-process t=0 - initial composition)(t-duration time of the r-process t=0 - initial composition)
Panov I Thielemann F-K Astronomy Letters Vol 30 (2004) 711
11 -delayed rates-delayed rates - - Pdf for Zlt100
22 (n(n)-rates )-rates Zlt115Zlt115
33 Neutron-induced fission rates Neutron-induced fission rates nifnif ~ lt ~ lt vgt vgt Zlt115
44 Spontaneous fission Spontaneous fission ndash phenomenologicalndash phenomenological models Zlt115 models Zlt115
55 -decay -decay Zlt115Zlt115
66 Mass predictions ETFSI HFB Thomas-Fermi Zlt115Mass predictions ETFSI HFB Thomas-Fermi Zlt115
77 ConclusionsConclusions
motivation further data reevaluation in the actinide and transactinide region
Bf lt Sn nuclei with Bf ge Sn inclined crosses nuclei with neutron binding energy predicted by the ETFSI [5] Sn sim 2 MeV and dots nuclei in which 2 gt Sn gt 0
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
fission
Main r-process R ge05 s cycling number ncycl (log2(YfinYinit)) gt 0 ~1
Model of Model of NSM-simulation Freiburghaus et al AJ 525 (1999)
Y(A) during r-process with fission cycling for NSM conditions Y(A) during r-process with fission cycling for NSM conditions (t-duration time of the r-process t=0 - initial composition)(t-duration time of the r-process t=0 - initial composition)
Panov I Thielemann F-K Astronomy Letters Vol 30 (2004) 711
11 -delayed rates-delayed rates - - Pdf for Zlt100
22 (n(n)-rates )-rates Zlt115Zlt115
33 Neutron-induced fission rates Neutron-induced fission rates nifnif ~ lt ~ lt vgt vgt Zlt115
44 Spontaneous fission Spontaneous fission ndash phenomenologicalndash phenomenological models Zlt115 models Zlt115
55 -decay -decay Zlt115Zlt115
66 Mass predictions ETFSI HFB Thomas-Fermi Zlt115Mass predictions ETFSI HFB Thomas-Fermi Zlt115
77 ConclusionsConclusions
motivation further data reevaluation in the actinide and transactinide region
Bf lt Sn nuclei with Bf ge Sn inclined crosses nuclei with neutron binding energy predicted by the ETFSI [5] Sn sim 2 MeV and dots nuclei in which 2 gt Sn gt 0
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Model of Model of NSM-simulation Freiburghaus et al AJ 525 (1999)
Y(A) during r-process with fission cycling for NSM conditions Y(A) during r-process with fission cycling for NSM conditions (t-duration time of the r-process t=0 - initial composition)(t-duration time of the r-process t=0 - initial composition)
Panov I Thielemann F-K Astronomy Letters Vol 30 (2004) 711
11 -delayed rates-delayed rates - - Pdf for Zlt100
22 (n(n)-rates )-rates Zlt115Zlt115
33 Neutron-induced fission rates Neutron-induced fission rates nifnif ~ lt ~ lt vgt vgt Zlt115
44 Spontaneous fission Spontaneous fission ndash phenomenologicalndash phenomenological models Zlt115 models Zlt115
55 -decay -decay Zlt115Zlt115
66 Mass predictions ETFSI HFB Thomas-Fermi Zlt115Mass predictions ETFSI HFB Thomas-Fermi Zlt115
77 ConclusionsConclusions
motivation further data reevaluation in the actinide and transactinide region
Bf lt Sn nuclei with Bf ge Sn inclined crosses nuclei with neutron binding energy predicted by the ETFSI [5] Sn sim 2 MeV and dots nuclei in which 2 gt Sn gt 0
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Y(A) during r-process with fission cycling for NSM conditions Y(A) during r-process with fission cycling for NSM conditions (t-duration time of the r-process t=0 - initial composition)(t-duration time of the r-process t=0 - initial composition)
Panov I Thielemann F-K Astronomy Letters Vol 30 (2004) 711
11 -delayed rates-delayed rates - - Pdf for Zlt100
22 (n(n)-rates )-rates Zlt115Zlt115
33 Neutron-induced fission rates Neutron-induced fission rates nifnif ~ lt ~ lt vgt vgt Zlt115
44 Spontaneous fission Spontaneous fission ndash phenomenologicalndash phenomenological models Zlt115 models Zlt115
55 -decay -decay Zlt115Zlt115
66 Mass predictions ETFSI HFB Thomas-Fermi Zlt115Mass predictions ETFSI HFB Thomas-Fermi Zlt115
77 ConclusionsConclusions
motivation further data reevaluation in the actinide and transactinide region
Bf lt Sn nuclei with Bf ge Sn inclined crosses nuclei with neutron binding energy predicted by the ETFSI [5] Sn sim 2 MeV and dots nuclei in which 2 gt Sn gt 0
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
11 -delayed rates-delayed rates - - Pdf for Zlt100
22 (n(n)-rates )-rates Zlt115Zlt115
33 Neutron-induced fission rates Neutron-induced fission rates nifnif ~ lt ~ lt vgt vgt Zlt115
44 Spontaneous fission Spontaneous fission ndash phenomenologicalndash phenomenological models Zlt115 models Zlt115
55 -decay -decay Zlt115Zlt115
66 Mass predictions ETFSI HFB Thomas-Fermi Zlt115Mass predictions ETFSI HFB Thomas-Fermi Zlt115
77 ConclusionsConclusions
motivation further data reevaluation in the actinide and transactinide region
Bf lt Sn nuclei with Bf ge Sn inclined crosses nuclei with neutron binding energy predicted by the ETFSI [5] Sn sim 2 MeV and dots nuclei in which 2 gt Sn gt 0
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Bf lt Sn nuclei with Bf ge Sn inclined crosses nuclei with neutron binding energy predicted by the ETFSI [5] Sn sim 2 MeV and dots nuclei in which 2 gt Sn gt 0
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
U Cm
Fm Z=104
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
sf - Smolanchuk et al
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
model-independent evaluations of model-independent evaluations of sf
bullBased on predicted Bf (GMartinec-Pinedo)
MS Lgsf = 23887 ndash 80824 x Bf
ETFSI Lgsf = 50127 - 10145 x Bf
bullBased on experimental values of Bf
Lgsf = 33 3 - 7 77 x Bfexp
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Lgsf = 33 3 - 7 77 x Bexp
f
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
If ltPdf gt ~ 50 then Ksurviv(from Z=94 to Z=114)~0000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
BETA - STRENGTH FUNCTION OF NEUTRON-RICH BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEINUCLEI
Fig 1 Schema of S (E) ndash for function for neutron-rich nuclei and -delayed processes
In calculation of weak process connected with -decay -absorption -delayed processes the Beta-Strength function S (E) plays the main role S (E) - function for neutron-rich nuclei
presented on Fig1
S (E)ndash function has a resonance
character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses Lower by energy are situated the so-called ldquopigmy resonansesrdquo The GTR with low going ldquotailrdquo influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities ldquoPigmy resonansesrdquo plays the main role in the T12 values -delayed neutron
emission -delayed fission and in neutron emission after neutrino- absorption process
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Calculation of Calculation of BetaBeta-Strength function in TFFS -Strength function in TFFS theorytheory
Beta-Strength function S (E) is formed by isobaric states in the Theory of Finite Fermy Systems
(TFFS) calculated solving the nuclear effective field equations of Gamov ndash Teller type
In this equations all types of particle-hole quasiparticle excitations are included except of l ndash forbidden type For the local single quasiparticle (στ) interaction g` constant used included pion-exchanging mode
222
2222
q0эф0 )q1(Rm
4
q1
q
d
dnfegg
In our low energy case (ΔEpnlt 20 MeV) the second pion-depending term is negligible For the
isovector constants f0 and g0 selfconsistent procedure was used Beta-Strength function S (E)
was calculated using matrix elements MGT
i iii
N
EГEE
EГEM
CES
4)()(
)()(
2)(
222
Normalization = Sum-rule S(E) dE = eq2 3 ( N - Z )
For Emax = 20 MeV and eq = 08 quenching value is q = 064 (for Emax = infin eq = 10 q = 10 )
Emax
0
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Quasiclassical Beta - ModelQuasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
where = -
21ll2 )r(Ra
212121 ll)(Rb
a 13
b = b+ + b- 23
31)A2(13
1b
A
ZN
E
E
ls
(j1-j2=1)
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Pa240 -gt U240
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Pa260 -gt U260
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Idn+df)
I = I
I = Idf
I + Idf + Idn ) =1
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
U -gt Np Beta ndash Delayed Fission ProbabilitiesU -gt Np Beta ndash Delayed Fission Probabilities TFFS-calculations (beta-model) TFFS-calculations (beta-model)
For dashed regions BfltEltSnf ~ tot Otherwise f ltlttot
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
BETA - DELAYED FISSIONBETA - DELAYED FISSION
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
P
bE
EEb
E
EEa
E
g
1
ls
ls
ls
ls
0
For BfltEltSn f ~ tot
Otherwise f ltlttot
where = -
21ll2 )r(Ra
212121 ll)(Rb
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
ConclusionsConclusionspredicted bd (and probably sf ) Rates predicted bd (and probably sf ) Rates looks overestimatedlooks overestimated
bull exp Data on superheavyexp Data on superheavy
bull Experimentally knowen branchings of beta-Experimentally knowen branchings of beta-deay (as well as theor Predictions) showdeay (as well as theor Predictions) show
aveage Intensity of beta-decays into low lying aveage Intensity of beta-decays into low lying states ~ 30states ~ 30
bull QRPA ndash predictions Pin ~ 80 ~ PbdfQRPA ndash predictions Pin ~ 80 ~ Pbdf
bull TFFS predictions Pin~ 60 and Pbdf ~ 20TFFS predictions Pin~ 60 and Pbdf ~ 20
Pin + Pbdf lt100Pin + Pbdf lt100
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Thank you for the Thank you for the attentionattention
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Isobaric Collective StatesIsobaric Collective States
TFFS equations follows Lane Theory of NucleusK Ikeda S Fujii and J I Fujita 1963-1967Gaponov amp Lutostansky 1972-1981
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
127127XeXe Beta-Strength functionBeta-Strength function
The comparison of measured and predicted S (E) ndash function for 127Xe
Breaking line ndash experimental data (1999) Solid line ndash TFFS calculations by Lutostansky and Shulgina (Phis Rev Lett 1991) GTR and low-lying ldquopigmyrdquo resonanses are well distinguishedThe experimental qwenching is q = 054 theoretical q = 064
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
ETFSI Lgsf = 50127 - 10145 Bf
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Pbdf Masses barriers ETFSI SPbdf Masses barriers ETFSI Sndash quasiclassical approach on ndash quasiclassical approach on
the basis of FFST(the basis of FFST(ТКФСТКФС) Gaponov Lutostansky Panov 1979) Gaponov Lutostansky Panov 1979
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Pa
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
bull
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
bull neutron-induced ndashneutron-induced ndash and - and -fission rates were calculated on fission rates were calculated on the basis of the nextthe basis of the next mass predictions and fission mass predictions and fission barriers TFETFSIFRDMHFB-14barriers TFETFSIFRDMHFB-14
bull
For explanation of yields in tnexplosionFor explanation of yields in tnexplosionbull Odd-even effect is reduced for HFB Odd-even effect is reduced for HFB predictionspredictionsbull The initial composition should consist from U The initial composition should consist from U
with admixture of some other actinides with admixture of some other actinides bull Inversion of odd-even effect can appear due Inversion of odd-even effect can appear due
both both df and Np (odd Z) admixture as welldf and Np (odd Z) admixture as wellbull Beta-delayed fission rates should be revisedBeta-delayed fission rates should be revised
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
4242
n n fissionfission competitioncompetitionPPdf df (SnBf1(1+exp(2 (Bf-E)h) )
Gs
n f
BfSn
Sn
n
γ
Bf
(ZA)(ZA)
(Z+1A)(Z+1A)
--
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Can we test the fission rates on the basis of Can we test the fission rates on the basis of the yields measured in impulse r-process the yields measured in impulse r-process experiments (thermonuclear explosions) experiments (thermonuclear explosions)
bull and what we can learn from the comparison and what we can learn from the comparison of calculated and experimental dataof calculated and experimental data
11 Compare results based on different Compare results based on different predictions (Masses Bpredictions (Masses Bff ) )
22 Test odd-even dependence and inversion of Test odd-even dependence and inversion of odd-even effectodd-even effect
33 Whether the (nf)-rates based on predicted Whether the (nf)-rates based on predicted fission barriers can fit the observed yieldsfission barriers can fit the observed yields
44 How the How the -delayed fission affect on -delayed fission affect on calculated yieldscalculated yields
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
R-processR-process Nuclear data I Nuclear data I bull Beta decay lifetimes and beta-delayed neutron emissionBeta decay lifetimes and beta-delayed neutron emission
bull PMoller JRNix K-LKratz ADNDT 66 (1997) 131PMoller JRNix K-LKratz ADNDT 66 (1997) 131 TT1212 P Pinin
bull (( n n)) and (n and (n ) rates ) rates RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83) RauscherampThielemann 2000 (Zlt84) Panov et al 2005 (Zgt83)
bull Neutron induced fission ratesNeutron induced fission rates Panov et al AampA (2010) Panov et al AampA (2010) bull Spontaneous fission Spontaneous fission rates rates (Smolanchuk et al (Smolanchuk et al
phenomenological models fphenomenological models f11(Z(Z22A) fA) f22(B(Bff) )) )bull Alpha-decay Alpha-decay ratesrates (Sobichevsky et al) (Sobichevsky et al)bull beta-delayed fission ratesbeta-delayed fission rates
Panov et al Nucl Phys A 747 (2005) 633 (Zlt101)Panov et al Nucl Phys A 747 (2005) 633 (Zlt101) data for Zgt100 neededdata for Zgt100 needed
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Nuclear data II mass and Nuclear data II mass and fission barrier predictionsfission barrier predictions
11 Masses - Extended Thomas-Fermi + Strutinsky Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI)integral (ETFSI)
ndash Y Aboussir JMPearson AK Dutta and FTondeur Y Aboussir JMPearson AK Dutta and FTondeur 19951995
bull Fission Barriers ndash ETFSi Fission Barriers ndash ETFSi ndash Mamdouh et al 2001Mamdouh et al 2001
22 Masses - Masses - Myers W D Swiatecki W JMyers W D Swiatecki W J 1996 1996bull Fission Barriers Fission Barriers Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
33 Masses ndash FRDM Masses ndash FRDM - - Moller PMoller P ADNDT v59 185 1995
bull Fission Barriers - Fission Barriers - Myers W D Swiatecki W JMyers W D Swiatecki W J 1999 1999
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
6 Data for the r-process (+SHE-6 Data for the r-process (+SHE-region)region)bull ETFSi mass and barrier predictions for Z up to 118ETFSi mass and barrier predictions for Z up to 118bull beta-rates for Zlt118 (QRPA+FRDM)beta-rates for Zlt118 (QRPA+FRDM)bull neutron-induced fission rates up to Z=115-118 neutron-induced fission rates up to Z=115-118
(will be published in AampA) and Available at CDS (will be published in AampA) and Available at CDS via httpcdswebu-strasbgfrcgi-binqcatJA+Abull Pdf for 90ltZlt100 ndash Krumlinde Moller 1984 qrpa (T12 - Kratz Moller Nix NP A 1997)bull Pdf for 100ltZlt110 were considered on the basis of
S calculated in framework of TFFS( model bull sf - phenomenological models or existed sf - phenomenological models or existed
calculations of Smolanchuk et alcalculations of Smolanchuk et al
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Lg(Tsf) s
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
IPetermann AArcones AKeliacutec KLanganke GMartiacutenez-Pinedo WSchmidt K-HHix I Panov T Rauscher F-K Thielemann NZinner NIC-2008
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
5151
HFTHFT ndash ndash parametrizations parametrizations used used
bull Double-humped fission barrier - Strutinskybull complete damping approximation which
averages over transmission resonancesbull levels in the second minimum are equally
spacedbull Hill-Wheeler transmission coefficient through a
parabolic barrierAB define the level densities above the saddle
points ABbull The back-shifted Fermi-gas description of the
level density was improved by introducing an energy dependent level density parameter a
bull The basis of experimentally known fission barriers was increased
bull deformed optical potentialbull The details are described in Rauscher amp The details are described in Rauscher amp
Thielemann ADNDT 2000 Panov et al NP 2005Thielemann ADNDT 2000 Panov et al NP 2005
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
R Smolanacuteczuk Acta Polonica 1999
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Smolanacuteczuk PHYSICAL REVIEW C VOLUME 56 812 (1997)
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
1 Mass and fission barriers predictions up to Z ~ 115 (ETFSI HFB TF)
2 (n)-rates for Z lt ~ 115
3 Neutron-induced fission rates nif ~ lt vgt for Zlt115
Panov et al AampA 2010 (extension to Rauscher and
Thielemann ADNDT 2000)
4 -delayed fission rates df for 90ltZlt101 Panov et al Nucl
Phys A 2005
5 spontaneous fission rates sf - from phenomenological rates to macro-micro
predictions (Sobichevski amp Pomorski 2007 Smolanchuk et al 1997)
6 and motivation
7 SHE modeling in the r-process
8 reevaluate -delayed fission rates df
9 Contribution of different fission types into nucleosynthesis
ReasonsReasons
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Beta ndash Delayed Multy-Neutron Beta ndash Delayed Multy-Neutron EmissionEmission
Q
B
Q
0nkn
kn
kn
dUdE)EU(W)U(IP
Probability for 2n - emission
U I(U) ndash energies and intensities in the daughter nucleus
Wn(U E) ndash probability of neutron emission
nBU
0infn
nfnn
)U(Г)U(q2dE)BEU(q)E(T
)BEU(q)E(T)EU(W
qi and qf ndash level densities of
compound and final nucleusТn(Е) mdash transitivity factor
Q
0 i
i
Q
B ijlmmn
ijl2
i
n2
dE)E(S)EQ1Z(f
dE)EE(W)E(S)EQ1Z(f
P n2
Probability for kn - emission
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
Beta ndash Delayed Fission CalculationsBeta ndash Delayed Fission Calculations
Q
0 i
i
Q
0 i tot
fi
f
dE)E(S)EQZ(f
dEГ
Г)E(S)EQZ(f
PProbabilities - Pβf d
4
)E(Г)EE(
)E(Г)E(M
2
C)E(S
22
ii
i2i
N
Beta Strength function
Г(Е) widths approximation Г(Е) = αE2 + βE3 + hellip
where α asymp 1εF and β laquo α so we used only the first term
As Гf laquo Гn so neutron emission dominates when this energetically possible
Sub-barrier fission probabilities in the daughter nucleus are small to gamma decay of exited states (barrier was taken in standard parabolic form) Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form
