Skyrme-RPA study of charged-current neutrino opacity in hot and dense supernova matter

Neutrino emission and their transport of energy to the supernova shock region are sensitive to the physics of hot and dense nuclear matter, which is a complex problem due to the strong correlations induced by nuclear forces. We derive charged-current opacities for electron neutrinos and antineutrinos in supernova matter using a self-consistent approach based on the Skyrme effective interaction. We include a mean field energy shift due to nuclear interaction and corrections due to RPA correlations. A complete treatment of the full Skyrme interaction, including a spin-orbit term, is given. To test the effect of RPA corrections, neutrino and antineutrino opacities are computed using different Skyrme parametrizations consistent with a number of infinite matter constraints.