Nuclear response functions with finite range Gogny force: tensor terms and instabilities

TL;DR

This paper uses advanced computational techniques to analyze nuclear matter response functions with Gogny forces, including tensor terms, revealing differences at higher-order calculations and assessing stability to guide future force development.

Contribution

It introduces a continued fraction method for response function calculation with Gogny forces, including tensor terms, and evaluates their stability and response characteristics.

Findings

Second order expansion shows significant differences for tensor-inclusive forces.

Most Gogny forces are free of spurious finite-size instabilities, except GT2.

Tensor terms cause heterogeneity in vector channel responses.

Abstract

A fully-antisymmetrized random phase approximation calculation employing the continued fraction technique is performed to study nuclear matter response functions with the finite range Gogny force. The most commonly used parameter sets of this force, as well as some recent generalizations that include the tensor terms are considered and the corresponding response functions are shown. The calculations are performed at the first and second order in the continued fraction expansion and the explicit expressions for the second order tensor contributions are given. Comparison between first and second order continued fraction expansion results are provided. The differences between the responses obtained at the two orders turn to be more pronounced for the forces including tensor terms than for the standard Gogny ones. In the vector channels the responses calculated with Gogny forces including tensor terms are characterized by a large heterogeneity, reflecting the different choices for the tensor part of the interaction. For sake of comparison the response functions obtained considering a G-matrix based nuclear interaction are also shown. As first application of the present calculation, the possible existence of spurious finite-size instabilities of the Gogny forces with or without tensor terms has been investigated. The positive conclusion is that all the Gogny forces, but the GT2 one, are free of spurious finite-size instabilities. In perspective, the tool developed in the present paper can be inserted in the fitting procedure to construct new Gogny-type forces.