Detection of the 4.4-MeV gamma rays from ${}^{16}$O($\nu ,{\nu }^{\prime }$)${}^{16}$O(12.97 $\mathrm{MeV},2^{-})$ with a water-Cherenkov detector in the supernova neutrino bursts

Abstract

We first discuss and determine the isospin mixing of the two $2^{-}$ states (12.53 MeV and 12.97 MeV) of ${}^{16}$O nucleus using the inelastic electron scattering data. We then evaluate the cross section of 4.4-MeV $\gamma$ rays produced in the neutrino neutral-current (NC) reaction ${}^{16}$O($\nu ,{\nu }^{\prime }$)${}^{16}$O$(12.97\mathrm{MeV},2^{-}$) in a water Cherenkov detector at the low energy below 100 MeV. The detection of $\gamma$ rays for $E_{\gamma }>5$ MeV from the NC reaction ${}^{16}$O($\nu ,{\nu }^{\prime }$)${}^{16}$O$(E_x>16\mathrm{MeV},T=1$) with a water Cherenkov detector in the supernova neutrino bursts has been proposed and discussed by several authors previously. In this article, we discuss a new NC reaction channel from ${}^{16}$O(12.97 $\mathrm{MeV},2^{-}$) producing a 4.4-MeV $\gamma$ ray, the cross section of which is more robust and even larger at the low energy ($E_{\nu }<25$ MeV) than the NC cross section from ${}^{16}$O$(E_x>16\mathrm{MeV},T=1$). We also evaluate the number of such events induced by neutrinos from supernova explosion which can be observed by the Super-Kamiokande, a 32 kton water Cherenkov detector in the Earth.

Comments: 23 Pages, 9 figures, Submitted for publication in PTEP journal on 13 November, 2022