Occupation numbers of spherical orbits in self-consistent beyond-mean-field methods

TL;DR

This paper introduces a method to calculate occupation numbers of spherical single-particle levels within the energy density functional framework, aiding comparisons with shell model results and guiding valence space definitions.

Contribution

The paper presents a novel approach to compute occupation numbers in self-consistent mean-field states, bridging EDF and shell model methods for better nuclear structure analysis.

Findings

Analyzed the onset of deformation in neutron-rich N=40 isotones.

Examined the role of SSP levels around N=40, especially in $^{64}$Cr.

Provided insights into the structure of neutron-rich nuclei.

Abstract

We present a method to compute the number of particles occupying spherical single-particle (SSP) levels within the energy density functional (EDF) framework. These SSP levels are defined for each nucleus by performing self-consistent mean-field calculations. The nuclear many-body states, in which the occupation numbers are evaluated, are obtained with a symmetry conserving configuration mixing (SCCM) method based on the Gogny EDF. The method allows a closer comparison between EDF and shell model with configuration mixing in large valence spaces (SM-CI) results, and can serve as a guidance to define physically sound valence spaces for SM-CI calculations. As a first application of the method, we analyze the onset of deformation in neutron-rich $N=40$ isotones and the role of the SSP levels around this harmonic oscillator magic number, with particular emphasis in the structure of $^{64}$Cr.