A COMPOSITE NUCLEAR-LEVEL DENSITY FORMULA WITH SHELL CORRECTIONS

TLDR

The authors develop a method to determine Fermi‑gas and low‑energy level‑density parameters using pairing and shell‑correction energies, fitting low‑energy levels and ensuring a smooth transition to the Fermi‑gas formula. They adopt a constant‑temperature representation at low excitation energies and a regular Fermi‑gas formula at high energies, and provide a composite prescription for calculating level densities in nuclei lacking experimental data. The procedure yields level densities at neutron‑binding energies with an average factor error of 1.8, reveals correlations between parameters and shell/pairing effects, supplies tables of level‑density parameters for many nuclei, and corrects slight errors in previous Fermi‑gas derivations.

Abstract

At low excitation energies a "constant nuclear temperature" representation of nuclear-level densities is used, and at high excitation energies the regular Fermi gas formula is adopted. A method is developed for determining the parameters of the Fermi gas formula by using both the pairing and the shell-correction energies found by Cameron and Elkin for their semiempirical atomic mass formula in its exponential form. This procedure determines level densities at neutron-binding-energy excitations subject to an average factor error of 1.8. Methods are also developed for determining the parameters for the lower-energy formula in such a way that it best fits the lower-energy levels and joins smoothly to the Fermi gas formula. Correlations of the resulting parameters with shell and pairing effects are found. A composite prescription is given for calculating level densities in nuclei for which no experimental information is known. Tables give level density parameters for a wide variety of nuclei for which some experimental information is known. Some of the derivations of the Fermi gas formula in the literature were found to be slightly incorrect, so new derivations are presented in Appendixes.