Neutrino-neutrino scattering and matter-enhanced neutrino flavor transformation in supernovae

We examine matter-enhanced neutrino flavor transformation (${\nu }_{\mathrm{\tau }\left(\mathrm{\mu }\right)\mathrm{?}}$ ${\nu }_{\mathit{e}}$) in the region above the neutrino sphere in type II supernovae. Our treatment explicitly includes contributions to the neutrino-propagation Hamiltonian from neutrino-neutrino forward scattering. A proper inclusion of these contributions shows that they have a completely negligible effect on the range of the ${\nu }_{\mathit{e}\mathrm{-}}$ ${\nu }_{\mathrm{\tau }\left(\mathrm{\mu }\right)}$ vacuum mass-squared difference δ${\mathit{m}}^2$, and vacuum mixing angle θ or equivalently ${\sin }^2$2θ, required for enhanced supernova shock reheating. When neutrino background effects are included, we find that r-process nucleosynthesis from neutrino-heated supernova ejecta remains a sensitive probe of the mixing between a light ${\nu }_{\mathit{e}}$ and a ${\nu }_{\mathrm{\tau }\left(\mathrm{\mu }\right)}$ with a cosmologically significant mass. Neutrino-neutrino scattering contributions are found to have a generally small effect on the (δ${\mathit{m}}^2$, ${\sin }^2$2θ) parameter region probed by r-process nucleosynthesis. We point out that the nonlinear effects of the neutrino background extend the range of sensitivity of r-process nucleosynthesis to smaller values of δ${\mathit{m}}^2$.