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

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

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

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

Effective-mass effects Bortignon+ Dasso

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

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

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

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<E*<245 MeV practically only complete fusion. Measured evaporation spectra gated on evaporation residues.

Level density and level-density parameters consistent with data.

Comparison to expectation

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

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

Al-Quaraishi et al. PRC (2001) fitted low- energy level-density data for 20<A<70 (Ohio Univ.) We have taken the liberty of extrapolating Al-Quraishi fitted forms to A~160 and high excitation energies to use as examples of isospin dependent level-density parameters.

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

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

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.

Constraint from triton/ 3 He ratio t/ 3 He ratio only probes isospin dependence at high excitation energies (100<E*<250 MeV). May not be relevant for r-process calculations.

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