Nuclear response for the Skyrme effective interaction with zero-range tensor terms. III. Neutron matter and neutrino propagation

TL;DR

This paper develops a formalism for analyzing the nuclear response in pure neutron matter using Skyrme functionals with tensor terms, and explores how these affect neutrino propagation and potential instabilities.

Contribution

It extends the linear response formalism to include tensor terms in Skyrme functionals for neutron matter and applies it to neutrino mean free path calculations.

Findings

Neutrino mean free path is highly sensitive to tensor terms.

Inverse energy weighted sum rule detects non-physical instabilities.

Analytical response functions are derived for all channels.

Abstract

The formalism of the linear response for the Skyrme energy density functional including tensor terms derived in articles [1,2] for nuclear matter is applied here to the case of pure neutron matter. As in article [2] we present analytical results for the response function in all channels, the Landau parameters and the odd-power sum rules. Special emphasis is given to the inverse energy weighted sum rule because it can be used to detect non physical instabilities. Typical examples are discussed and numerical results shown. Moreover, as a direct application, neutrino propagation in neutron matter is investigated through its neutrino mean free path at zero temperature. This quantity turns out to be very sensitive to the tensor terms of the Skyrme energy density functional.