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We study neutrino-nucleon scattering and absorption in a dense, magnetizednuclear medium. These are the most important sources of neutrino opacitygoverning the cooling of a proto-neutron star in the first tens of secondsafter its formation. Because the weak interaction is parity violating, theabsorption and scattering cross-sections depend asymmetrically on thedirections of the neutrino momenta with respect to the magnetic field. Wedevelop the moment formalism of neutrino transport in the presence of suchasymmetric opacities and derive explicit expressions for the neutrino flux andother angular moments of the Boltzmann transport equation. For a given neutrinospecies, there is a drift flux of neutrinos along the magnetic field inaddition to the usual diffusive flux. This drift flux depends on the deviationof the neutrino distribution function from thermal equilibrium. Hence, despitethe fact that the neutrino cross-sections are asymmetric throughout the star,asymmetric neutrino flux can be generated only in the outer region of theproto-neutron star where the neutrino distribution deviates significantly fromthermal equilibrium. In addition to the asymmetric absorption opacity arisingfrom nucleon polarization, we find the contribution of the electron (orpositron) ground state Landau level. For neutrinos of energy less than a fewtimes the temperature, this is the dominant source of asymmetric opacity.Lastly, we discuss the implication of our result to the origin of pulsar kicks:in order to generate kick velocity of a few hundred km/s from asymmetricneutrino emission using the parity violation effect, the proto-neutron starmust have a dipole magnetic field of at least $10^{15}-10^{16}$ G.Comment: 35 pages, no figures, submitted to Phys.Rev.

Neutrino-nucleon interactions in magnetized neutron-star matter: The effects of parity violation