Neutrino-nucleon scattering in supernova matter from the virial expansion

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 SV and spin SA responses. We find that SA is significantly reduced from one even at low densities. We provide a simple fit SAf(n,T,Yp) of the axial response as a function of density n, temperature T, and proton fraction Yp, 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.