Semiclassical shell-structure micro-macroscopic approach for the level density: https://arxiv.org/abs/2103.16480
A.G. Magner, A.I. Sanzhur, S.N. Fedotkin, A.I. Levon, S. Shlomo
Nuclear level density ρ(E,A) is derived for a nuclear system with a given energy E and particle number A within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method, obtaining ρ∝Iν(S)/Sν, where Iν(S) is the modified Bessel function of the entropy S. Within the micro-macrocanonical approximation (MMA), for a small thermal excitation energy, U, with respect to rotational excitations, Erot, one obtains ν=3/2 for ρ(E,A). In the case of larger excitation energy U but smaller the neutron separation energy, one finds a larger value of ν=5/2. A role of the fixed spin variable for rotating nuclei is discussed. The MMA level density ρ reaches the well-known grand-canonical ensemble limit (Fermi gas asymptotics) for large S related to large excitation energies, and the finite micro-canonical limit for small combinatorical entropy S at low excitation energies (constant "temperature" model). Fitting the MMA ρ(E,A) to the experimental data and taking into account shell and, qualitatively, pairing effects for low excitation energies, one obtains the inverse level density parameter K, which differs essentially from that deduced from data on neutron resonances.
Comments: 20 pages, 4 figures, 1 Table