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Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
A. Brondi, G. La Rana, R. Moro, M. Trotta, E. Vardaci
Università di Napoli Federico II,
and Istituto Nazionale di Fisica Nucleare, Napoli, Italy
Search for isospin effects on nuclear level density
The Physics Opportunities with Eurisol
Trento, January 16-20, 2006
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Why is it important to study the level density ?
Level density is a basic ingredient for x-section calculations
Astrophysical processes “Astrophysical Reaction Rates from Statistical Model Calculations”, ADNDT 75 (2000) 1-351
SHE’s production
Capture of two nuclei in the attractive potential pocket.
ER capture PCN Psurv
Survival probability against fission.
Probability of forming a compact compound nucleus (CN).
Fluctuation-dissipation dynamics: Fokker-Plank or Langevin equations
Evaporative process: Statistical Model
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Study of isospin effects on level density through fusion-evaporation reactions
Temperature, Angular momentum, Pairing & Shell effects: a ,
Isopin (?)
Isospin comes in through: Isospin Distribution
Symmetry Energy
P(Uo,Jo,l,U,J) (U,J) . Tl(
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Isospin distribution
A reduction of level density with increasing |T3| is predicted
Statistical mechanics
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Level densities in n-rich and n-deficient nuclei Isospin distribution
20<A<70 ENSDF
Form A:
Form B:
Form C:
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Level density in n-deficient Dy nuclei
n-rich n-deficient
140Dy
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Study of the level density in n-deficient Dy nuclei
•Which observables?
“… complete level schemes up to 2.5 MeV will be difficult to obtain for higher A and for nuclei far off the valley of stability. Thus further tests of this level density approach will likely be based on evaporation spectra…”Al Quraishi et al., Phys. Rev. C 63, 065803
Method: observation of evaporative xp channels Observables: E.R. yields and energy spectra
•To what extent such effects on level density can be observed?
Statistical model calculations (Lilita_N97)
76Kr + 64Zn 140Dy Ex = 50 MeV - xp channels
Standard a = A/8,
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Study of level density in n-deficient Dy nuclei
Enhanced effects
using Z-Zo prescription
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Study of level density in n-deficient Dy nuclei
Decay channels involving a small
number of particles – Low Ex
St. N-Z Z-ZO
p (b) 1.3 0.32 1322
1n (b) 1.3 1.3 225
1(b) 1890 3500 2478
Owing to the higher average
energy, 1particle decay
channels are enhanced
using Z-Zo prescription
Best condition:
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Why is it important to study the symmetry energy ?
Esym=bsym(T)(N-Z)2/A
• As a part of the nuclear Equation Of State it may influence the mechanism of Supernova explosion
• General theoretical agreement on its temperature dependence (LRT+QRPA vs. large scale SMMC)
• Possible consequences of T dependence of Esym on core-collapse Supernova events still debated
• Effects enhanced by the instrinsic isospin dependence of Esym
Fusion-evaporation reactions: Esym affects the particle B.E.
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
SYMMETRY ENERGY
m(T) 0 < T < 3 MeV - 98Mo, 64Zn, 64Ni
-Hartree-Fock – coupling s.p.s. to c.v.
-LRT – QRPA
Decrease of the effective mass Increase of Esym
Esym(T)= bsym(T) x (N-Z)2/A
bsym(T)=bsym(0)+(h2ko2m/6mk)[m(T)-1 – m(0)-1]
m(T)=m + [m(0) – m]exp(-T/To)
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Study of the level density in n-rich Mo nuclei
Method: observation of evaporative xn channels (1n, 2n)Observables: E.R. yields and energy spectra
Statistical model calculations (Lilita_N97)
105Zr + 4He 109Mo Ex = 14-20 MeV - 1n, 2n channels
98Kr + 12C 110Mo Ex = 50-85 MeV - 5n, 6n channels
Standard a = A/8,
Symmetry energy: prescription of P. Donati et al.
Isospin distribution:
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Symmetry energy and isospin distribution effects
Esym effect
dominates
at low Ex
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Moving to higher excitation energies
1
10
100
1000
10000
40 45 50 55 60 65 70 75 80 85 90
Ex(MeV)
fus(mb)
Lfus(h)
98Kr + 12C 110Mo Elab=285 - 605 MeV
More channels involved, including charged particleemission
Higher cross sections
Higher angular momenta(mb)
J(h)
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Single effects on different evaporative channels
No effects are observed for Esym
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Isospin effects on energy spectra shapes
No effects are observed for Esym
5n channel
1n channel
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
In program…..
- Refinements of the model: microscopic level density based on single-particle level schemes obtained from Hartree-Fock calculations on the basis of the Gogny effective interaction, taking into account for parity, angular momentum, pairing corrections as well as collective enhancements. S. Hilaire et al., Eur. Phys. J. A, 169 (2001)
- Estention of calculations to other exotic nuclei
- Measurements with existent RIB and SB facilities
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Summary and perspectives
• The availability of n-rich and n-deficient RNB’s will allow to study isospin effects on fusion-evaporation reactions. These may have strong implications in nuclear astrophysics and affect the estimation of SHE’s production cross sections.
• Such studies require:
- High intensity n-rich and p-rich beams
- High selectivity, high granularity, high efficiency detectors
• Such tasks may be accomplished using:
- SPES, SPIRAL II, EURISOL beams
- Neutron + Charged particle detectors; High efficiency, large solid angle ER separators (PRISMA in GFM, VAMOS); Gamma tracking arrays (AGATA).
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Testing realistic effective interactions on exotic nuclei around closed shells
Covello, L. Coraggio, A. Gargano, and N. Itaco
Università di Napoli Federico II,
and Istituto Nazionale di Fisica Nucleare, Napoli, Italy
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Theory
B(E2;0+ 2+) = 0.033 e2b2
134Sn Coulex (Oak Ridge)
B(E2;0+ 2+) = 0.029(4) e2b2
Expt. Theory
726 keV
Lowest first-excited2+ level in semi-magiceven-even nuclei
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Theory
B(E2;0+ 2+) = 0.18 e2b2
136Te Coulex (Oak Ridge)
B(E2;0+ 2+) = 0.103(15) e2b2
New measurement larger value: ~ 0.13(15) e2b2
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Theory with free g-factors: B(M1) = 25 x 10-3 (n.m.)2
Theory with effective M1 operator: 4 x 10-3 (n.m)2
B(M1;5/2+ 7/2+) = 0.29 x 10-3 (n.m.)2 (OSIRIS, Studsvik)
N/Z = 1.65 : most exotic nucleus beyond 132Sn for which there is information on excited states
From 133Sb: ε5/2 = 962 keV
282 keV
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Mechanism of Supernova explosion
• When the n-rich core of a massive star reaches a mass limit, it begins to collapse.
• The increased density induces electron captures on both free protons and protons bound in nuclei, driving the matter in the core towards successively more n-rich nuclei.
• As long as the density remains lower than the “trapping density”, the neutrinos produced escape freely from the core, releasing energy.
Influence of symmetry energy:• The larger the symmetry energy, the more difficult is to change protons
into neutrons.
• Via the EOS, the symmetry energy influences the amount of free protons in the core, that in the late stage of the collapse are believed to be the main source for electron capture.
Larger symmetry energy smaller electron capture rate less energy lost by neutrino escape stronger shock wave
Supernova explosion
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Isospin effects on ……
105Zr + 4He 109Mo
98Kr + 12C 110Mo
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Isospin effects on 1n and 2n channel yields
105Zr + 4He 109Mo