Unified approach to structure factors and neutrino processes in nucleon matter

We present a unified approach to neutrino processes in nucleon matter based on Landau's theory of Fermi liquids that includes one and two quasiparticle-quasihole pair states as well as mean-field effects. We show how rates of neutrino processes involving two nucleons may be calculated in terms of the collision integral in the Landau transport equation for quasiparticles. Using a relaxation time approximation, we solve the transport equation for density and spin-density fluctuations and derive a general form for the response functions. We apply our approach to neutral-current processes in neutron matter, where the spin response function is crucial to the calculation of neutrino elastic and inelastic scattering and neutrino-pair bremsstrahlung and absorption from strongly interacting nucleons. We calculate the relaxation rates using modern nuclear interactions and including many-body contributions, and find that rates of neutrino processes are reduced compared with estimates based on the one-pion exchange interaction, which is used in current simulations of core-collapse supernovae.