A. Brondi, G. La Rana, R. Moro, M. Trotta, E. Vardaci

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The Physics Opportunities with Eurisol Trento,
January 16-20, 2006
Search for isospin effects on nuclear level
density
A. Brondi, G. La Rana, R. Moro, M. Trotta, E.
Vardaci Università di Napoli Federico II, and
Istituto Nazionale di Fisica Nucleare, Napoli,
Italy
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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
SHEs production

Capture of two nuclei in the attractive potential
pocket.
Survival probability against fission.
Probability of forming a compact compound nucleus
(CN).
Fluctuation-dissipation dynamics
Fokker-Plank or Langevin equations
Evaporative process Statistical Model
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Study of isospin effects on level density
through fusion-evaporation reactions
P(Uo,Jo,e,l,U,J) ? r(U,J) . Tl(e)
Temperature, Angular momentum, Pairing Shell
effects a , s, d Isopin (?) Isospin comes in
through Isospin
Distribution
Symmetry Energy
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Isospin distribution
Statistical mechanics
A reduction of level density with increasing T3
is predicted
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Level densities in n-rich and n-deficient nuclei
Isospin distribution
20ltAlt70 ENSDF
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Level density in n-deficient Dy nuclei
n-rich
n-deficient
140Dy
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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,
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Study of level density in n-deficient Dy nuclei
Enhanced effects using Z-Zo prescription
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Study of level density in n-deficient Dy nuclei
Best condition
Decay channels involving a small number of
particles Low Ex
St. N-Z Z-ZO
s1p (mb) 1.3 0.32 1322
s1n (mb) 1.3 1.3 225
s1a (mb) 1890 3500 2478
Owing to the higher average energy, 1particle
decay channels are enhanced using Z-Zo
prescription
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Why is it important to study the symmetry energy ?

• Esymbsym(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 (LRTQRPA 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.
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SYMMETRY ENERGY
mw(T) 0 lt T lt 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)mw(T)-1
mw(0)-1 mw(T)m mw(0) mexp(-T/To)
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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
Isospin distribution
Standard a A/8,
Symmetry energy prescription of P. Donati et
al.
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Effect of symmetry energy
Effect
EX
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Symmetry energy and isospin distribution effects
Esym effect dominates at low Ex
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Moving to higher excitation energies
Higher cross sections Higher angular momenta
s(mb)
J(h)
More channels involved, including charged
particle emission
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Single effects on different evaporative channels
No effects are observed for Esym
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Isospin effects on energy spectra shapes
5n channel
1n channel
No effects are observed for Esym
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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
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Summary and perspectives

• The availability of n-rich and n-deficient RNBs
  will allow to study isospin effects on
  fusion-evaporation reactions. These may have
  strong implications in nuclear astrophysics and
  affect the estimation of SHEs 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).

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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

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Lowest first-excited 2 level in
semi-magic even-even nuclei
726 keV
Expt.
Theory
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(No Transcript)
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(No Transcript)
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From 133Sb e5/2 962 keV
282 keV
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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
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Isospin effects on
105Zr 4He ? 109Mo
98Kr 12C ? 110Mo
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Isospin effects on 1n and 2n channel yields
105Zr 4He ? 109Mo
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Single effects on different evaporative channels
No effects are observed for Esym