Pairing correlations within the micro-macroscopic approach for the level density

Level density ρ (E,N,Z) is calculated for the two-component close- and open-shell nuclei with a given energy E , and neutron N and proton Z numbers, taking into account pairing effects within the microscopic-macroscopic approach (MMA). These analytical calculations have been carried out by using semiclassical statistical mean-field approximations beyond the saddle-point method of the Fermi gas model in a low excitation-energies range. The level density ρ , obtained as function of the system entropy S , depends essentially on the condensation energy E_cond through the excitation energy U in super-fluid nuclei. The simplest super-fluid approach, based on the BCS theory, accounts for a smooth temperature dependence of the pairing gap Δ due to particle number fluctuations. Taking into account the pairing effects in magic or semi-magic nuclei, excited below neutron resonances, one finds a notable pairing phase transition. Pairing correlations sometimes improve significantly the comparison with experimental data.