Neutrino-nucleon scattering in supernova matter from the virial expansion

Abstract

We extend 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 that $S_A$ is significantly reduced from one even at low densities. We provide a simple fit $S^f_A$ ($n , T , Y_p$) of the axial response as a function of density $n$ , temperature $T$ , and proton fraction $Y_p$ , which can be incorporated into supernova simulations in a straightforward manner. This fit reproduces our virial results at low densities and the Burrows and Sawyer random-phase approximation (RPA) model calculations at high densities. Preliminary one-dimensional supernova simulations suggest that the virial reduction in the axial response may enhance neutrino heating rates in the gain region during the accretion phase of a core-collapse supernovae.