Nuclear Level Densities in the Constant-Spacing Model

TL;DR

This paper introduces a new analytical method for calculating nuclear level densities in the constant-spacing model, improving accuracy over Gaussian approximations by incorporating higher moments, and validated against numerical results.

Contribution

Develops a sixth-moment analytical approximation for nuclear level densities in the constant-spacing model, enhancing accuracy over traditional Gaussian methods.

Findings

Gaussian form of densities for large particle/hole numbers

Sixth-moment approximation matches numerical results well

Effective across all excitation energies and particle/hole configurations

Abstract

A new method to calculate level densities for non-interacting Fermions within the constant-spacing model with a finite number of states is developed. We show that asymptotically (for large numbers of particles or holes) the densities have Gaussian form. We improve on the Gaussian distribution by using analytical expressions for moments higher than the second. Comparison with numerical results shows that the resulting sixth-moment approximation is excellent except near the boundaries of the spectra and works globally for all particle/hole numbers and all excitation energies.