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Anatoli AfanasjevMississippi State University, USA
GRETA/GRETINA: physical challenges – view of theorist
1. How do protons and neutrons interact to form nuclei?2. What are the origins of simple patterns in complex nuclei?3. What are the limits of angular momentum, excitation
energy, charge and mass for nuclei?4. What is the origin of elements?
Basic physics questions to GRETINA/GRETA
Single-particle degrees of freedom
GRETINA will have a factor of about 8 improvement in resolving powerrelative to GAMMASPHERE for lower multiplicity processes, such as Coulombexcitations and transfer reactions … … will greatly expand the opportunitiesfor advancing nuclear structure studies to higher spin, heavier mass, and to odd-A nuclei; all cases where the density of gamma-ray transitions exceeds the energy resolution achieved using present day gamma-ray detectors for in-beam spectroscopy
From GRETINA proposal
1. Single-particle properties of heaviest actinides better understanding of physics of superheavy nuclei
2. Single-particle properties of very neutron-rich nuclei better mass tables, better predictions for neutron-drip line, better understanding of
physics of neutron-rich nuclei
Experimental Experimental quasiparticlequasiparticlestates provide states provide
1. Important constraint for the 1. Important constraint for the selection of effective forces forselection of effective forces forthe description of the description of superheavysuperheavy
nucleinuclei2. Provide information about2. Provide information aboutspherical spherical subshellssubshells (high(high--j)j)
active in the vicinity of expectedactive in the vicinity of expectedshells gaps in spherical shells gaps in spherical superheavysuperheavy
A.V.Afanasjev et al, PRC 67 (2003) 024309
Analysis allowedAnalysis allowedto exclude the to exclude the NLSHNLSH andandNLRA1NLRA1 RMF forces fromRMF forces from
further applicationfurther applicationto to superheavysuperheavy nucleinuclei(the only sets which (the only sets which
predict Z=114 as shell gap)predict Z=114 as shell gap)
Quasiparticle spectra in heaviest actinide nuclei
corrected by the empirical shifts obtained in the detailed study of quasiparticlespectra in odd-mass nuclei of the deformed A~250 mass region (PRC 67 (2003) 024309)
SelfSelf--consistentconsistentsolutionsolution
RMF analysis of singleRMF analysis of single--particle energies in spherical Z=120, N=172 nucleusparticle energies in spherical Z=120, N=172 nucleus
RMFRMFdouble shell closure double shell closure
at Z=120,N=172at Z=120,N=172
SkyrmeSkyrme SkPSkP [m*/m=1][m*/m=1]double shell closuredouble shell closureat Z=126, N=184at Z=126, N=184
((SkMSkM*, *, ????????
SkyrmeSkyrme SkI3 [m*/m=0.57]SkI3 [m*/m=0.57]gaps at Z=120, N=184gaps at Z=120, N=184no double shell closure,no double shell closure,
SLy6SLy6
GognyGogny D1SD1SZ=120, N=172(?)Z=120, N=172(?)
Z=126, N=184Z=126, N=184
Low
eff
ectiv
e m
ass
Low
eff
ectiv
e m
ass
m*/
m ~
0.6
5m
*/m
~ 0
.65
Larg
e ef
fect
ive
Larg
e ef
fect
ive
mas
s m
*/m
~0.
8m
ass
m*/
m~
0.8 --
1.0
1.0
Which role effective mass plays???Which role effective mass plays???
Large density depressionLarge density depressionin the central part of nucleus:in the central part of nucleus:shell gaps at Z=120, shell gaps at Z=120,
N=172N=172
Flat density distributionFlat density distributionin the central part of nucleus:in the central part of nucleus:
Z=126 appears, Z=126 appears, N=184 becomes larger N=184 becomes larger
and Z=120and Z=120(N=172) shrinks(N=172) shrinks
Physics of neutron rich nuclei
S. Goriely, J.M.Pearson and Co
Skyrme functional: fit to masses allowedto decrease rms deviation (on masses) from~ 2.5 MeV down to ~ 0.7 MeV. In total ~20 parameters fitted to several thousands
of nuclei.Open questions: 1. No unique fit (how this affects the r-process abundancies???)
2. Should we use single-particleproperties as an additional
constraint on effective force?
Single-particle information has to be taken into account in orderto improve the quality of effective interactions (and probably, find missing channels of interactions) in the self-consistent theories.
Summary on single-particle properties
Example: extrapolability of mass tables to unknown nucleiFRDM (Moller, Nix) – good, rms error remains the sameSHF (S. Goriely, J.M.Pearson and Co) – deteriorates for older
parametrizations, unknown for newest ones From J.Rikowska-Stone, J.Phys. G: 31 (2005) R211
Principal difference between FRDM and SHF: careful fit of single-particledegrees of freedom.
There are > 80 Skyrme and > 40 RMF parametrizations, but they were fitted with no single-particle information taken into account.
Theory: careful fit of lowest single-particle states in deformednuclei within ‘a la table of mass’ strategy
Experiment: s-p states in heaviest deformed nuclei +s-p states in deformed neutron-rich nuclei
Jacobi transition
Rotational damping
Hyperdeformation
Order-chaostransition
FissionSpin limit
Spin
Normal-deformed(terminating)
Superdeformed(non-terminating)
Energy
(Near-)spherical
High-spin laboratory
# of p-h excitationsdeformation‘maximum’ spin
in the configuration
Rotating nuclei: the best laboratory for study of shape coexistence starting from spherical ground state
by means of subsequent particle-hole excitations one canbuild any shape (prolate and oblate [collective and
non-collective], triaxial, superdeformed, hyperdeformedetc.)
Termination and non-termination of rotationalbands
- basic feature of shell model- important feature of a finite many-fermion quantum mechanical system which either do not exist or cannot be experimentally measured in other quantum systems
Q1: Do all rotational bands end up in terminating states? How the transition from terminating to non-terminating bands takes place?
Q2. How the terminating states of smooth terminating bands are fed? (experimental proof of their termination)
Do all rotational bands end up in terminating states ???Do all rotational bands end up in terminating states ???T.Troudet and R. Arvieu, Ann. Phys. 134, 1 (1981)
Imax – the maximum spin which can be built in the pure configuration
Rotational bands do not terminatein a noncollective state at Imax if the deformation exceeds a critical
value at low spin.
Terminate Do not terminate
Cranked harmonic oscillator
Origin: due to the coupling of different N shells leading to a
mixing of different configurations
Even higher spins than Imax canbe build within the mixed
configuration.
Theoretical models:•CNS: Cranked Nilsson-Strutinsky
•CRMF: Cranked Relativistic Mean Field
No non-collective state can be defined for
I>Imax
Potential energy
surfaces for the GSB
configuration
Imax
Super- and hyperdeformation in neutron-rich nuclei.
- Mean field is well justified + pairing correlations are expectedto have negligible impact at high spin = clean probe of
effective interactions
Q1: How effective interactions are modified by neutron excessand fast rotation?
SD(2) is built on ph excitation acrossthe Z=48 SD shell gap. Crossing freq.
confirm its existence.
AA, S.Frauendorf, PRC 72 (2005) 031301(R)
J(2) of HD configurations = 67-71 MeV-1
N=60 and 62 SD shell gaps in CRMF.
SD(1)
SD(2)
-First hints for Hyperdeformation(“ridges” in γ−γ spectra)
compound nucleus at the highest spinsmost neutron-rich stable isotopes
48Ca + 82Se 126Xe + 4n
similar to the first observation of superdeformation ~20 years ago
Observation of hyperdeformed nucleiGamma-ray tracking arrayhigh intensity neutron-rich beams
Hyperdeformation
Superdeformation in nuclei around 68Zn
Hyperdeformation in the A~120-130 mass region
B. Herskind et al
Ridge structures in 3-D rotational mapped spectra are identifiedwith dynamic moments of inertia J(2) ranging from 71 to 111 MeV-1
Experiment:Wild variations of J(2): example 122Xe J(2)=77 MeV-1
124Xe J(2)=111 MeV-1
Preliminary CRMF: 122Xe J(2) (HD) ~ 75 MeV-1
Due to Z=30 and N=38 SD shell gaps
See M. Devlin et al, PRL 82 (1999) 5217
The presence or absenceof exotic nuclear shapes(swiss cheese, spaghetti
and lasagna phases) beforetransition to uniform npematter depends on the
assumed model of effective nucleon-nucleon interaction
‘SD’ and ‘HD’ in the crust of neutron stars
Rotating systems: the best laboratory
for time-odd mean fields
Time-odd mean fieldsOpen questions:dependence on deformation,configuration, spin, isospin etc. ????Method: to eliminate the uncertainties related to pairing use high-spin data
Impact of time-odd meanfields (in %)
Wobbling motion
Q1: Can wobbling excitations be observed in other regionsof nuclear chart in which theoretical calculations strongly
suggests the existence of triaxial shapes at high spin?
Q2: What are the basic conditions for the existence of wobbling excitations?
- unique signal of triaxiality of nuclei
110110Sb Sb yrastyrast band configuration band configuration [21,3] = [#[21,3] = [# gg9/29/2
--11 ## hh11/211/2, #, # hh11/211/2]]
see A.V.Afanasjev, D.B.Fossan, G.J. Lane and I.Ragnarsson, Physics Report 322 (1999) 1
Theoretical calculations suggests that many rotational bands possess appreciable triaxiality over considerable spin range:
1. Smooth terminating bands in the A~110 and A~60 mass regions
2. Many normal- and highly deformed rotational bands in the A~60-80 and A~130 mass regions
3. Superdeformed bands in the A~80 mass region
D.G.Sarantites et al,PRC 57 (1998) R1
Wobbling motion
Wobbling excitations were not observed in these regionsof nuclear chart so far !!!
Possible reasons:1. Do not exist in these nuclei. Why?
2. Wobbling excitations in are highly non-yrast in these nuclei??? Will GRETA be able to measure such
excitations?
Giant Resonances
The GDR position has been measured for about 90 stable nucleiall lying on beta stability line.Extend these measurement to 1. Unstable neutron- and proton-rich nuclei2. To high spin systems