Neutrino production and transport during gravitational collapse

The P--N method is developed to describe the transport of neutrinos in collapsing stellar cores, and the multigroup flux limited diffusion and equilibrium diffusion approximations are obtained from it. An effective Lagrangian for weak neutral and charged current neutrino interactions which is applicable to low energy neutrino processes is derived. The neutrino source functions which enter into the P--N equations are given a many body theory formulation in terms of weak current--current correlation functions. Within this framework, in turn, the scattering reactions νA → νA, νA → νA*, νN → νN (both for nondegenerate and degenerate nucleons), νe → νe, and νν → νν, and the production and absorption reactions e-p reversible nν/sub e/, e+n reversible p antiν/sub e/, e-/sup A/Z reversible /sup A/(Z-1)ν/sub e/, e+e- reversible ν anti ν, and γ/sub pl/ reversible ν anti ν are dealt with in turn. These equations are then applied to the various phases of neutrino flow during iron core collapse: the transparent stage to the onset of trapping; the approach to electron neutrinos to beta-equilibrium; the evolution of the muon neutrino and antineutrino distribution functions towards the Fermi--Dirac form; the conditions under which ν/sub μ/anti ν/sub μ/diative energy loss exceeds the ν/sub e/ loss; comparison of the P-1 and flux limited diffusion methods of spatial transport in a static pre-bounce core