Shell-structure and asymmetry effects in level densities

TL;DR

This paper derives a semiclassical formula for nuclear level densities incorporating shell effects and asymmetry, revealing how these factors influence the density's behavior across different energy regimes.

Contribution

It introduces a novel semiclassical approach using extended Thomas-Fermi and periodic-orbit theory to model nuclear level densities with shell and asymmetry effects beyond traditional methods.

Findings

Level density follows a modified Bessel function form with shell effects influencing the parameter .

The micro-macroscopic approximation yields different  values depending on shell contribution strength.

Fitted models to experimental data show significant deviations in the inverse level density parameter from neutron resonance values.

Abstract

Level density $\rho(E,N,Z)$ is derived for a nuclear system with a given energy $E$, neutron $N$, and proton $Z$ particle numbers, within the semiclassical extended Thomas-Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain $~~\rho \propto I_\nu(S)/S^\nu$,~~ where $I_\nu(S)$ is the modified Bessel function of the entropy $S$, and $\nu$ is related to the number of integrals of motion, except for the energy $E$. For small shell structure contribution one obtains within the micro-macroscopic approximation (MMA) the value of $\nu=2$ for $\rho(E,N,Z)$. In the opposite case of much larger shell structure contributions one finds a larger value of $\nu=3$. The MMA level density $\rho$ reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA $\rho(E,N,Z)$ to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter $K$, which differs significantly from that of neutron resonances.