Semiclassical shell-structure micro-macroscopic approach for the level density

Level density rho(E, A) is derived for a one-component nucleon system with a given energy E and particle number A within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method of the Fermi gas model. We obtain rho proportional to I-nu(S)/S-nu, with I-nu(S) being the modified Bessel function of the entropy S. Within the micro-macro-canonical approximation (MMA), for a small thermal excitation energy U, with respect to rotational excitations E-rot, one obtains nu = 3/2 for rho(E, A). In the case of excitation energy U larger than Erot but smaller than the neutron separation energy, one finds a larger value of nu = 5/2. A role of the fixed spin variables for rotating nuclei is discussed. The MMA level density rho reaches the well-known grand-canonical ensemble limit (Fermi gas asymptote) for large S related to large excitation energies, and also reaches the finite micro-canonical limit for small combinatorial entropy S at low excitation energies (the constant "temperature" model). Fitting the rho(E, A) of the MMA to the experimental data for low excitation energies, taking into account shell and, qualitatively, pairing effects, one obtains for the inverse level density parameter K a value which differs essentially from that parameter derived from data on neutron resonances.