Neutrino-nucleon scattering in supernova matter from the virial expansion

TL;DR

This paper extends the virial approach to analyze neutrino-nucleon scattering in supernova matter, providing model-independent low-density predictions and a practical fit for supernova simulations, indicating potential impacts on neutrino heating.

Contribution

It introduces a generalized virial method for neutrino response in supernova matter, including a simple fit for the axial response applicable across densities and conditions.

Findings

S_A is significantly reduced from one at low densities

The fit S_A^f matches virial and RPA results across densities

Reduction in axial response may enhance neutrino heating in supernovae

Abstract

We generalize our virial approach to study the neutral current neutrino response of nuclear matter at low densities. In the long-wavelength limit, the virial expansion makes model-independent predictions for neutrino-nucleon scattering rates and the density S_V and spin S_A responses. We find S_A is significantly reduced from one even at low densities. We provide a simple fit S_A^f(n,T,Y_p) of the axial response as a function of density n, temperature T and proton fraction Y_p. This fit reproduces our model independent virial results at low densities and reproduces the Burrows and Sawyer random phase approximation (RPA) results at high densities. Our fit can be incorporated into supernova simulations in a straight forward manner. Preliminary one dimensional supernova simulations suggest that the reduction in the axial response may enhance neutrino heating rates in the gain region during the accretion phase of a core-collapse supernovae.