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Supernova explosions are the most powerful neutrino sources. The neutrinoemission 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 alsoto some extent its angle distribution. We therefore study the energy and angledependence of neutrino scattering rates in proto-neutron star and supernovamatter with the full Skyrme RPA response functions. We confirm earlier findingsobtained in the Landau approximation that the RPA reduces neutrino scattering,but the detailed differential scattering rates in hot and dense matter dependsensitively on the adopted interaction. The scattering angle distribution isdifferent for different interactions because it depends strongly on the neutronFermi velocity. We also find that many Skyrme interactions present anunphysical feature that the Fermi velocity of neutrons exceeds the speed oflight already at relatively low densities.

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