Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force

TL;DR

This paper introduces a novel computational method combining triaxial angular momentum projection and configuration mixing with the Gogny force, applied to magnesium-24, achieving good agreement with experimental data.

Contribution

It is the first implementation of the generator coordinate method with full triaxial angular momentum and particle number projection using the Gogny force in the $(eta, ext{gamma})$ plane.

Findings

Accurate energy levels for $^{24}$Mg's excited states.

Good agreement of transition probabilities with experimental data.

Effective description of ground and gamma bands without strong mixing.

Abstract

We present the first implementation in the $(\beta,\gamma)$ plane of the generator coordinate method with full triaxial angular momentum and particle number projected wave functions using the Gogny force. Technical details about the performance of the method and the convergence of the results both in the symmetry restoration and the configuration mixing parts are discussed in detail. We apply the method to the study of $^{24}$Mg, the calculated energies of excited states as well as the transition probabilities are compared to the available experimental data showing a good overall agreement. In addition, we present the RVAMPIR approach which provides a good description of the ground and gamma bands in the absence of strong mixing.