A symmetry conserving description of odd-nuclei with the Gogny force

TL;DR

This paper introduces a symmetry-conserving method for calculating properties of odd-nuclei using the Gogny force, achieving good agreement with experimental data for $^{31}$Mg.

Contribution

It develops a self-consistent approach with exact blocking and projection techniques for odd-nuclei using the finite-range Gogny force, which is a novel application.

Findings

Accurately reproduces ground state properties of $^{31}$Mg.

Successfully describes excited states and transition probabilities.

Provides a reliable framework for odd-nuclei calculations.

Abstract

We present an approach for the calculation of odd-nuclei with exact self-consistent blocking and particle number and angular momentum projection with the finite range density dependent Gogny force. As an application we calculate the nucleus $^{31}$Mg at the border of the $N=20$ inversion island. We evaluate the ground state properties, the excited states and the transition probabilities. In general we obtain a good description of the measured observables.