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

TL;DR

This paper calculates nuclear level densities considering pairing effects within a microscopic-macroscopic framework, revealing the impact of superfluidity and pairing correlations on nuclear properties at low excitation energies.

Contribution

It introduces an analytical method for level density calculation that incorporates pairing effects using semiclassical approximations beyond the saddle-point method.

Findings

Level density depends on condensation energy and entropy.

Pairing effects cause a smooth temperature dependence of the pairing gap.

Pairing correlations can significantly improve agreement with experimental data.

Abstract

Level density $\rho(E,N,Z)$ 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 the semiclassical statistical mean-field approximations beyond the saddle-point method of the Fermi gas model in a low excitation-energies range. The level density $\rho$, obtained as function of the system entropy $S$, depends essentially on the condensation energy $E_{\rm cond}$ 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 $\Delta$ 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.