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

We examine matter-enhanced neutrino flavor transformation ([nu][sub [tau]([mu])[r reversible]][nu][sub [ital 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][sub [ital e]-][nu][sub [tau]([mu])] vacuum mass-squared difference [delta][ital m][sup 2], and vacuum mixing angle [theta] or equivalently sin[sup 2]2[theta], required for enhanced supernova shock reheating. When neutrino background effects are included, we find that [ital r]-process nucleosynthesis from neutrino-heated supernova ejecta remains a sensitive probe of the mixing between a light [nu][sub [ital e]] and a [nu][sub [tau]([mu])] with a cosmologically significant mass. Neutrino-neutrino scattering contributions are found to have a generally small effect on the ([delta][ital m][sup 2], sin[sup 2]2[theta]) parameter region probed by [ital r]-process nucleosynthesis. We point out that the nonlinear effects of the neutrino background extend the range of sensitivity of [ital r]-process nucleosynthesis to smaller values of [delta][ital m][sup 2].