Chemical potential effects on neutrino diffusion in supernovae

The validity of imposing a zero chemical potential for neutrinos in hydrodynamic calculations of collapsing supernovae is investigated in the diffusion approximation of neutrino transport. A coupled system of equations is solved for neutrino and energy diffusion fluxes as well as lepton diffusion in a collapsing supernovae ambient medium, and the results indicate a substantial growth in the neutrino chemical potential for densities greater than 10 to the 12th power gm/cu cm. The rate of energy transport is shown to be significantly affected by increases in Fermi integrals and chemical-potential gradients accompanied by decreases in temperature, and the extent of neutrino particle/antiparticle reactions is found also to affect energy diffusion rates. It is concluded that the photon-like behavior usually assumed for neutrinos may be incorrect and that an extension of the Sn transport approximation to include lepton characteristics is necessary for a definitive answer to the question of neutrino transport in supernovae.