We examine matter-enhanced neutrino flavor transformation ($ν_{τ(μ)}\rightleftharpoonsν_e$) 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 $ν_e$-$ν_{τ(μ)}$ vacuum mass-squared difference, $δm^2$, and vacuum mixing angle, $θ$, or equivalently $\sin^22θ$, 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 $ν_e$ and a $ν_{τ(μ)}$ with a cosmologically significant mass. Neutrino-neutrino scattering contributions are found to have a generally small effect on the $(δm^2,\ \sin^22θ)$ 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 $δm^2$.

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