Inconsistencies in the description of pairing effects in nuclear level densities

TL;DR

This paper examines inconsistencies in how pairing effects are described in nuclear level densities, highlighting conflicts between empirical models and nuclear properties, and proposes modifications and more realistic theories.

Contribution

It identifies discrepancies in existing phenomenological and theoretical descriptions of pairing effects and suggests improvements for more accurate modeling.

Findings

Back-shift parameter inconsistencies with stable pairing correlations

Incompatibility of pairing condensation energies in BCS model for light nuclei

Proposed modifications to Gilbert-Cameron level-density description

Abstract

Pairing correlations have a strong influence on nuclear level densities. Empirical descriptions and theoretical models have been developed to take these effects into account. The present article discusses cases, where descriptions of nuclear level densities are inconsistent or in conflict with the present understanding of nuclear properties. Phenomenological approaches consider a back-shift parameter. However, the absolute magnitude of the back-shift, which actually corresponds to the pairing condensation energy, is generally not compatible with the observation that stable pairing correlations are present in essentially all nuclei. It is also shown that in the BCS model pairing condensation energies and critical pairing energies are inconsistent for light nuclei. A modification to the composite Gilbert-Cameron level-density description is proposed, and the use of more realistic pairing theories is suggested.