Neutrino-nucleon scattering in the neutrino-sphere

TL;DR

This paper calculates the neutrino scattering rates in hot neutron matter relevant to supernovae and neutron star mergers, revealing how nucleon interactions influence neutrino decoupling through dynamical structure factors.

Contribution

First calculation of dynamical structure factors for neutron matter using virial expansion, incorporating nucleon-nucleon correlations to improve neutrino scattering models.

Findings

Attractive s-wave interactions enhance density response.

Correlations suppress spin response and backscattering.

Scaling laws enable analytic structure factor calculations.

Abstract

We calculate the differential scattering rate for thermal neutrinos in a hot and dilute gas of interacting neutrons using linear response theory. The dynamical structure factors for density and spin fluctuations of the strongly interacting neutron matter, expected in the neutrino decoupling regions of supernovae and neutron star mergers, are calculated in the virial expansion for the first time. Correlations due to nucleon-nucleon interactions are taken into account using a pseudo-potential that reproduces measured nucleon-nucleon phase shifts, and we find that attractive s-wave interactions enhance the density response and suppress the spin response of neutron matter. The net effect of neutron correlations is to strongly suppress backscattering. Moreover, we find nearly exact scaling laws for the response functions, valid for the range $T = 5 - 10$ MeV and q < 30 MeV, allowing us to obtain analytic results for the dynamic structure factors at second-order in the fugacity of the neutron gas. We find that the modification of scattering rates depends on the energy and momentum exchanged, implying that dynamical structure factors are essential to describe neutrino decoupling in supernovae and neutron star mergers.