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Using the results of a high precision calculation of the solar neutrinosurvival probability for Earth crossing neutrinos in the case of MSW $\nu_e \to\nu_{\mu(\tau)}$ transition solution of the solar neutrino problem, performedin 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 withthe Super - Kamiokande detector, and for the D-N asymmetry in the energy-integrated one year signal in this detector. The asymmetries are calculated forsolar $\nu_e$ 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 solutionregion obtained by taking into account possible uncertainties in the values ofthe $^8$B and $^7$Be neutrino fluxes. The effect of the uncertainties in thevalue 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, thatfor $\sin^2 2\theta_v \leq 0.013$ the one year average D-N asymmetry forneutrinos crossing the Earth core can be larger than the asymmetry for (onlymantle 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 theSuper - Kamiokande detector are derived in the region $\sin^2 2\theta_v \gsim10^{-4}$ for only mantle crossing, core crossing and (only mantle crossing +core crossing) neutrinos. Our results indicate that the Super - Kamiokandeexperiment might be able to test the $\sin^2 2\theta_v \le 0.01$ region of theMSW solution of the solar neutrino problem by performing selective D-Nasymmetry measurements.Comment: LaTeX, 18 pages, 3 Tables, 16 Figures in 7 postscript file

Study of the day-night effect for the Super-Kamiokande detector. II. Electron spectrum deformations and day-night asymmetries