Spurious finite-size instabilities with Gogny-type interactions

TL;DR

This paper investigates the presence of spurious finite-size instabilities in the new D1M* Gogny interaction, revealing unphysical results in nuclear calculations and emphasizing the importance of linear response methods in interaction parameter fitting.

Contribution

It is the first study to identify and analyze finite-size instabilities in the D1M* Gogny interaction using RPA calculations and tests against mean-field results.

Findings

D1M* exhibits spurious finite-size instabilities in the scalar isovector channel.

Unphysical nuclear properties are observed when using D1M* and D1N parameterizations.

Linear response formalism is recommended for detecting instabilities during Gogny force parameter fitting.

Abstract

Recently, a new parameterization of the Gogny interaction suitable for astrophysical applications, named D1M*, has been presented. We investigate the possible existence of spurious finite-size instabilities of this new Gogny force by repeating a study that we have already performed for the most commonly used parameterizations (D1, D1S, D1N, D1M) of the Gogny force. This study is based on a fully-antisymmetrized random phase approximation (RPA) calculation of the nuclear matter response functions employing the continued fraction technique. It turns out that this new Gogny interaction is affected by spurious finite-size instabilities in the scalar isovector channel; hence, unphysical results are expected in the calculation of properties of nuclei, like neutron and proton densities, if this D1M* force is used. The conclusions from this study are then, for the first time, tested against mean-field calculations in a coordinate representation for several nuclei. Unphysical results for several nuclei are also obtained with the D1N parameterization of the Gogny force. These observations strongly advocate for the use of the linear response formalism to detect and avoid finite-size instabilities during the fit of the parameters of Gogny interactions as it is already done for some Skyrme forces.