Does the Gogny interaction need a third Gaussian?

TL;DR

This paper proposes adding a third Gaussian to the Gogny interaction's central part, based on infinite matter constraints, to improve its accuracy and applicability.

Contribution

It introduces a statistical method to determine the optimal parameters for a third Gaussian in the Gogny interaction, enhancing its theoretical foundation.

Findings

A third Gaussian improves the Gogny interaction's consistency with infinite matter constraints.

Statistical analysis identifies parameter ranges compatible with physical constraints.

The proposed modification potentially enhances the interaction's predictive power.

Abstract

By considering infinite matter constraints only, we suggest in this paper that the Gogny interaction should benefit from a third Gaussian in its central part. A statistical analysis is given to select the possible ranges which are compatible with these constraints and which minimize a $\chi^2$ function.