Neutrino self-interaction and MSW effects in supernovae and the $\nu$-process

We consider the modification of the neutrino spectrum and luminosity from core-collapse supernovae both by the neutrino self-interaction near the neutrinosphere and the Mikheyev-Smirnov-Wolfenstein effect in the outer layers. We show the effects of these interactions on the gain radius in the delayed neutrino heating of the supernova. We also consider the impact of these modification to the neutrino spectrum on the $\nu$-process nucleosynthesis in the outer parts of the star. We find that the abundances of $^7$Li and the heavy isotopes $^{92}$Nb, $^{98}$Tc and $^{138}$La are reduced by a factor of $\sim 2$ by the $\nu$-self-interaction. In contrast, $^{11}$B is relatively insensitive. We also find that the abundance ratio of heavy to light nuclei, $^{138}$La/$^{11}$B, is a possible new probe of the neutrino mass hierarchy, and that the normal mass hierarchy is slightly favored by solar meteoritic abundances.