  In the previous work, we discussed the cross section and the detection of
4.4-MeV $\gamma$ rays produced in the neutrino neutral-current (NC) reaction
$^{16}$O($\nu, \nu^{\prime}$)$^{16}$O(12.97 MeV and 12.53 MeV, $2^-$) in a
water Cherenkov detector at the low energy below 100 MeV. In this report, we
further investigated both the charged-current (CC) reaction
$^{16}$O($\bar\nu_e, e^+$)$^{16}$N(0 MeV, $2^-$) and the NC
reaction$^{16}$O($\nu, \nu^{\prime}$)$^{16}$O(12.97 MeV and 12.53 MeV, $2^-$),
producing high-energy $\gamma$ rays, in which the more solid identification of
the reactions can be applied via the coincidence method.
