Nuclear response for the Skyrme effective interaction with zero-range tensor terms. II. Sum rules and instabilities

TL;DR

This paper extends linear response theory for Skyrme interactions with tensor terms to infinite matter and uses sum rules, especially $M_{-1}$, to identify potential instabilities in Skyrme functionals.

Contribution

It generalizes the formalism for Skyrme energy density functionals with tensor terms and provides analytical tools to detect instabilities via sum rules.

Findings

Analytical expressions for odd-power sum rules derived.

$M_{-1}$ sum rule effectively detects instabilities.

Extended formalism applicable to infinite nuclear matter.

Abstract

The formalism of linear response theory for Skyrme forces including tensor terms presented in article [1] is generalized for the case of a Skyrme energy density functional in infinite matter. We also present analytical results for the odd-power sum rules, with particular attention to the inverse energy weighted sum rule, $M_{-1}$, as a tool to detect instabilities in Skyrme functionals.