Tools for incorporating a D-wave contribution in Skyrme energy density functionals

TL;DR

This paper develops tools to incorporate a D-wave term into Skyrme energy density functionals, enabling improved modeling of nuclear interactions and stability analysis in spherical nuclei.

Contribution

It provides a mean-field equation and response function tools to include the D-wave term in Skyrme functionals for better nuclear modeling.

Findings

Tools for incorporating D-wave terms into Skyrme functionals.

Method to detect unphysical instabilities in spherical nuclei.

Framework for fitting new functional parameters.

Abstract

The possibility of adding a D-wave term to the standard Skyrme effective interaction has been widely considered in the past. Such a term has been shown to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential. The aim of the present article is to provide the necessary tools to incorporate this term in a fitting procedure: first, a mean-field equation written in spherical symmetry in order to describe spherical nuclei and second, the response function to detect unphysical instabilities. With these tools it will be possible to build a new fitting procedure to determine the coupling constants of the new functional.