Nuclear weak interactions, supernova nucleosynthesis and neutrino oscillation

We study the nuclear weak response in light-to-heavy mass nuclei and calculate neutrino-nucleus cross sections. We apply these cross sections to the explosive nucleosynthesis in core-collapse supernovae and find that several isotopes of rare elements ⁷Li, ¹¹B, ¹³⁸La, ¹⁸⁰Ta and several others are predominantly produced by the neutrino-process nucleosynthesis. We discuss how to determine the suitable neutrino spectra of three different flavors and their anti-particles in order to explain the observed solar system abundances of these isotopes, combined with Galactic chemical evolution of the light nuclei and the heavy r-process elements. Light-mass nuclei like ⁷Li and ¹¹B, which are produced in outer He-layer, are strongly affected by the neutrino flavor oscillation due to the MSW (Mikheyev-Smirnov-Wolfenstein) effect, while heavy-mass nuclei like ¹³⁸La, ¹⁸⁰Ta and r-process elements, which are produced in the inner O-Ne-Mg layer or the atmosphere of proto-neutron star, are likely to be free from the MSW effect. Using such a different nature of the neutrino-process nucleosynthesis, we study the neutrino oscillation effects on their abundances, and propose a new novel method to determine the unknown neutrino oscillation parameters, θ₁₃ and mass hierarchy, simultaneously. There is recent evidence that some SiC X grains from the Murchison meteorite may contain supernova-produced neutrino-process ¹¹B and ⁷Li encapsulated in the grains. Combining the recent experimental constraints on θ₁₃, we show that although the uncertainties are still large, our method hints at a marginal preference for an inverted neutrino mass hierarchy for the first time.