NEUTRINO FLAVOR EVOLUTION NEAR A SUPERNOVAS CORE

In supernovae and in the early universe, neutrino flavor evolution is a many-body phenomena. Here the equations describing the evolution of the density matrices in phase space are derived. Then these equations are applied to neutrino emission from a supernova core. The effects of a ''small'' background neutrino density on adiabatic and nonadiabatic flavor evolution are calculated analytically. It is found that when flavor evolution is sizeable, the sensitivity to the small neutrino background is enhancer. This implies that r-process nucleosynthesis in supernovae may not reliably probe neutrino masses less than about 25 eV.