Effects of nuclear forces on neutrino opacities in hot nuclear matter

Neutrino opacities are analyzed in terms of correlation functions for density, spin density, isospin density, and spin-isospin density operators. In a long-wavelength limit appropriate to the scattering of thermal neutrinos in most situations relevant to the supernova, the opacities coming from the neutral current interaction are given in terms of susceptibilities, ∂${\rho }_i$/∂${\mu }_j$, where ${\rho }_i$ are the various densities and ${\mu }_j$ the associated chemical potentials. These susceptibilities are calculated in the framework of a Skyrme interaction, one which has been used in calculations of the hot equation of state, supplemented by spin-dependent terms from other sources. There is a large reduction in the Gamow-Teller part of the cross sections in all of the domains of temperature, proton fraction, and density which were studied. Effects of the screened Coulomb force also cause a large reduction in the opacity arising from the Fermi interaction of the neutrino with protons, in some domains of density and temperature.