A Study of the Day - Night Effect for the Super-Kamiokande Detector: II. Electron Spectrum Deformations and Day - Night Asymmetries

Using the results of a high precision calculation of the solar neutrino survival probability for Earth crossing neutrinos in the case of MSW $\nu_e \to \nu_{\mu(\tau)}$ transition solution of the solar neutrino problem, performed in an earlier study, we derive predictions for the one-year averaged day-night (D-N) asymmetry in the deformations of the $e^-$ - spectrum to be measured with the Super - Kamiokande detector, and for the D-N asymmetry in the energy- integrated one year signal in this detector. The asymmetries are calculated for solar $\nu_e$ crossing the Earth mantle only, the core and the (mantle + core) for a large representative set of values of the MSW transition parameters $\Delta m^2$ and $\sin^2 2\theta_v$ from the ``conservative'' MSW solution region obtained by taking into account possible uncertainties in the values of the $^8$B and $^7$Be neutrino fluxes. The effect of the uncertainties in the value of the bulk matter density and in the chemical composition of the core, on the D-N asymmetry predictions is discussed. It is shown, in particular, that for $\sin^2 2\theta_v \leq 0.013$ the one year average D-N asymmetry for neutrinos crossing the Earth core can be larger than the asymmetry for (only mantle crossing + core crossing) neutrinos by a factor of up to six. Iso - (D-N) asymmetry contours in the $\Delta m^2 - \sin^2 2\theta_v$ plane for the Super - Kamiokande detector are derived in the region $\sin^2 2\theta_v \gsim 10^{-4}$ for only mantle crossing, core crossing and (only mantle crossing + core crossing) neutrinos. Our results indicate that the Super - Kamiokande experiment might be able to test the $\sin^2 2\theta_v \le 0.01$ region of the MSW solution of the solar neutrino problem by performing selective D-N asymmetry measurements.