Nuclear Level Densities at High Excitation Energies and for Large Particle Numbers

TL;DR

This paper develops an analytical approximation for nuclear level densities at high excitation energies, using moments and cumulants, applicable for large nuclei and covering a broad energy spectrum.

Contribution

It introduces a new asymptotic analytical method to estimate nuclear level densities based on moments and orthogonal polynomial expansions, valid for large mass numbers.

Findings

Accurately approximates level densities over 20 orders of magnitude.

Applicable to large nuclei with mass number A >> 1.

Covers about half the spectrum near the maximum density.

Abstract

Starting from an independent-particle model with a finite and arbitrary set of single-particle energies, we develop an analytical approximation to the many-body level density $\rho_A(E)$ and to particle-hole densities. We use exact expressions for the low-order moments and cumulants to derive approximate expressions for the coefficients of an expansion of these densities in terms of orthogonal polynomials. The approach is asymptotically (mass number $A \gg 1$) convergent and, for large $A$, covers about 20 orders of magnitude near the maximum of $\rho_A(E)$ (i.e., about half the spectrum). Densities of accessible states are calculated using the Fermi-gas model.