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

TL;DR

This paper develops a semiclassical approach to calculate nuclear level density, extending the Fermi gas model with periodic-orbit theory, and compares results with experimental data, revealing new insights into nuclear excitation and shell effects.

Contribution

It introduces a semiclassical shell-structure micro-macroscopic model for nuclear level density beyond the Fermi gas approximation, incorporating spin and shell effects.

Findings

Derived a new expression for level density involving Bessel functions.

Identified different regimes of level density depending on excitation energy.

Compared model predictions with experimental data, highlighting differences in inverse level density parameters.

Abstract

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 $~~\rho \propto I_\nu(S)/S^\nu$, 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, $E_{\rm rot}$, one obtains $\nu=3/2$ for $\rho(E,A)$. In the case of excitation energy $U$ larger than $E_{\rm rot}$ 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 asymptotic) 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.