Neutrino-Neutrino Scattering and Matter-Enhanced Neutrino Flavor Transformation in Supernovae

Abstract

We examine matter-enhanced neutrino flavor transformation (${\nu }_{\tau (\mu )}\rightleftharpoons {\nu }_e$) 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 ${\nu }_e$-${\nu }_{\tau (\mu )}$ vacuum mass-squared difference, $\delta m^2$, and vacuum mixing angle, $\theta$, or equivalently ${\sin }^{2}2\theta$, required for enhanced supernova shock re-heating. 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 ${\nu }_e$ and a ${\nu }_{\tau (\mu )}$ with a cosmologically significant mass. Neutrino-neutrino scattering contributions are found to have a generally small effect on the $(\delta m^2,{\sin }^{2}2\theta )$ 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 $\delta m^2$.

38 pages, tex, DOE/ER/40561-150-INT94-00-63

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