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Temperature and isospin dependencies of the level-density parameter. Robert Charity Washington University in St. Louis

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Why are level densities important? govern the statistical decay of excited nuclei can tell about the properties of such nuclei as they contain many-body effects needed for nucleosynthesis calculations (r-process), reactor science, stockpile stewardship program

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Fermi-gas level-density expressions 1) Single-particle model, no many-body effects 2) Used in most statistical-model calculations.

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Collective enhancement (many-body effect) Bjornholm,Bohr,Mottleson,Ignatyuk Collective Rotational bands are build on each intrinsic or single-particle state. (for a deformed system) Collective rotations can be considered as a coherent superposition of single-particle states and thus they must be included in r FG. However many-body effects push these states down in energy giving rise to the enhancement, but the enhancement must fade out at high energies (otherwise double counting). Also collective vibrational enhancement. r FG Junghans et al. claim evidence for collective enhancement in fragmentation yields

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Effective-mass effects Bortignon+ Dasso

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Expected excitation-energy dependence of the level-density parameter loss of collective enhancement excitation-energy dependence from many-body effects decreasing effective mass A/10 =intrinsic a (Ignatyuk) A/7-A/8 (neutron resonance counting) A/13 50 MeV loss of collective enhancement 250 MeV a eff A=160

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How do we measure the level density at high excitation energies.

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Temperature can be obtained from the exponential slope of kinetic-energy spectra of evaporated particles First-chance emission Account for multichance emission with statistical-model calculations with GEMINI

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Fit experimental spectra with GEMINI simulations Cannot fit with constant “a” Reactions= 60 Ni+ 100 Mo, 60 Ni+ 92 Mo 5 < E/A<9 MeV 91

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Level density and level-density parameters consistent with data.

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Comparison to expectation

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Extracted a(t) is consistent with calculations of Shlomo +Natowitz PRC (1991) (No collective enhancement effects)

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Isospin dependence of level density parameter If there is a significantly larger dependence it will be important for r-process. In the Fermi-gas model there is a very small isospin dependence

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Al-Quaraishi et al. PRC (2001) fitted low- energy level-density data for 20

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Case B A t 3 =(Z-N)/2=0 nucleus has t=0,1,2,… levels A t 3 =1 nucleus has t=1,2 ….. levels A t 3 =2 nucleus has t=2, ….. levels t 3 =0 nuclei has the most levels Case C (continuum effects) What is the single-particle level density for g(e), e>0? If we only count long-lived resonances, g is suppressed. Level-density suppressed if m~0 i.e., near drip line Level-density maximum at b -valley of stability

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Evaporation attractor line With no isospin dependent level density. The action of evaporation on the location in the chart of nuclides of a hot system is move it towards a line called the Evaporation attractor line (on average) One cannot cross the attractor line. PRC (1998) Experimentally determine mean location of residues from multiplicities of evaporated n,p,d,t, 3 He, a

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Effect of isospin-dependent level density The average location of the residues can cross the attractor line! Hanold et al PRC 1462 (1995) measured neutron-poor residues from E/A=50 MeV 129 Xe+ 27 Al incomplete- fusion reactions with Average location of residues is on the neutron-poor side of the attractor line.

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Constraint from triton/ 3 He ratio t/ 3 He ratio only probes isospin dependence at high excitation energies (100

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Conclusions Confirm that the level-density parameter is temperature or excitation-energy dependent. We are starting to probe this dependence in more detail. We see a decrease in the parameter with excitation energy consistent with the calculations of Shlomo + Natowitz. Have not yet seen any evidence of fade-out of collective enhancement. Junghans et al. claim evidence for it in study of fragmentation yields of isotopes nears closed shells. If there is an isospin dependence of the level-density parameter, it is quite small for the neutron-deficient systems studied at excitation energies from 100 to 250 MeV. Collaboration with Washing Univ Indiana Univ. Oregon State Univ. Argonne Nat. Lab. Charity,Sobotka,Dempsey, Devlin,Komarov,Sarantites, Caraley,DeSouza,Loveland, Peterson,Back,Davids, Seweryniak

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