Energy and Angle Dependence of Neutrino Scattering Rates in Proto-Neutron Star and Supernova Matter within Skyrme RPA

Supernova explosions are the most powerful neutrino sources. The neutrino emission is also the dominating cooling mechanism for a proto-neutron star, whose interior is mainly composed of extremely dense and hot nuclear matter. Neutrino transport is an essential part of the simulation of these phenomena, and modern codes are able to implement inelastic neutrino scattering and also to some extent its angle distribution. We therefore study the energy and angle dependence of neutrino scattering rates in proto-neutron star and supernova matter with the full Skyrme RPA response functions. We confirm earlier findings obtained in the Landau approximation that the RPA reduces neutrino scattering, but the detailed differential scattering rates in hot and dense matter depend sensitively on the adopted interaction. The scattering angle distribution is different for different interactions because it depends strongly on the neutron Fermi velocity. We also find that many Skyrme interactions present an unphysical feature that the Fermi velocity of neutrons exceeds the speed of light already at relatively low densities.