Constraints on Neutrino Mixing from r-process Nucleosynthesis in Supernovae

In this paper we note that for neutrino mass squared differences in the range $10^{-4} - 10^{-1} eV^2$, vacuum neutrino oscillations can take place between the neutrino-sphere and the weak freeze-out radius in a type II supernova. Requiring that such oscillations are consistent with the r-process nucleosynthesis from supernovae one can constrain the mixing of $\nu_e$ with $\nu_{\mu}$ (or $\nu_\tau$) down to $10^{-4} eV^2$. We first do a two-flavor study and find that the neutron rich condition $Y_e < 0.5$ is satisfied for all values of mixing angles. However if we take the criterion $Y_e < 0.45$ for a successful r-process and assume $\nu_\mu - \nu_e$ oscillations to be operative then this mode as a possible solution to the atmospheric neutrino anomaly is ruled out in accordance with the recent CHOOZ result. Furthermore since we can probe mass ranges lower than CHOOZ the narrow range that was allowed by the CHOOZ data at 99% C.L. is also ruled out. Next we do a three-generation analysis keeping $\Delta m_{12}^2 \sim 10^{-5} eV^2$ or $10^{-11} eV^2$ (solar neutrino range) and $\Delta m_{13}^2 \approx \Delta m_{23}^2 \sim 10^{-4} - 10^{-1} eV^2$ (atmospheric neutrino range) and use the condition $Y_e < 0.45$ to give bounds on the mixing parameters and compare our results with the CHOOZ bound. We also calculate the increase in the shock-reheating obtained by such oscillations.