Effects of correlations on neutrino opacities in nuclear matter

Including nucleon-nucleon correlations due to both Fermi statistics and nuclear forces, we have developed a general formalism for calculating the neutral-current neutrino-nucleon opacities in nuclear matter. We derive corrections to the dynamic structure factors due to both density and spin correlations and find that neutrino-nucleon cross sections are suppressed by large factors around and above nuclear density. In addition, we find that the spectrum of energy transfers in neutrino scattering is considerably broadened by the interactions in the medium. An identifiable component of this broadening comes from the absorption and emission of quanta of collective modes akin to the Gamow-Teller and Giant Dipole resonances in nuclei (zero-sound; spin waves), with \v{C}erenkov kinematics. Under the assumption that both the charged-current and the neutral-current cross sections are decreased by many-body effects, we calculate a set of ad hoc protoneutron star cooling models to gauge the potential importance of the new opacities to the supernova itself. We find that after many hundreds of milliseconds to seconds the driving neutrino luminosities might be increased by from 10% to 100%. However, the actual consequences, if any, of these new neutrino opacities remain to be determined.