Linear response theory and neutrino mean free path using Brussels-Montreal Skyrme functionals

TL;DR

This paper extends linear response theory with new Skyrme functionals to calculate neutrino mean free paths in neutron matter, comparing results with ab-initio methods to improve understanding of nuclear matter properties.

Contribution

It introduces an extended formalism incorporating additional density-dependent terms in Skyrme functionals at finite temperature for neutrino interactions.

Findings

Predictions align with ab-initio calculations.

Extended functionals improve modeling of neutron matter.

Neutrino mean free path estimates are provided.

Abstract

The Brussels-Montreal Skyrme functionals have been successful to describe properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predictions from the Brussels-Montreal Skyrme functionals are compared with ab-initio methods.