Effects of correlations on neutrino opacities in nuclear matter

Abstract

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 scattering rates in nuclear matter. We derive corrections to the dynamic structure factors due to both density and spin correlations and find that neutrino-nucleon scattering rates are suppressed by large factors around and above nuclear density. Hence, in particular for the ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ neutrinos, but also for the ${\ensuremath{\nu}}_{e}$ neutrinos, supernova cores are more ``transparent'' than previously thought. The many-body corrections increase with density, decrease with temperature, and are roughly independent of incident neutrino energy. 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 sound), with \ifmmode \check{C}\else \v{C}\fi{}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. While the early luminosities are not altered, the luminosities after many hundreds of milliseconds to seconds can be increased by factors that range from 10 to 100 %. Such enhancements may have a bearing on the efficacy of the neutrino-driven supernova mechanism, the delay to explosion, the energy of the explosion, and the strength and relative role of convective overturn at late times. However, the actual consequences, if any, of these new neutrino opacities remain to be determined.