Study of the day-night effect for the Super-Kamiokande detector .1. Time-averaged solar neutrino survival probability

This is the first of two articles aimed at providing comprehensive predictions for the day-night (D-N) effect for the Super-Kamiokande detector in the case of the Mikheyev-Smirnov-Wolfenstein (MSW) upsilon(e)-->upsilon(mu(tau)) transition solution of the solar neutrino problem. The one-year-averaged probability of survival of the solar upsilon(e) crossing the Earth's mantle, the core, the inner 2/3 of the core, and the (core+mantle) is calculated with high precision (better than 1%) using the elliptical orbit approximation to describe the Earth's motion around the Sun. Results for the survival probability in the indicated cases are obtained for a large set of values of the MSW transition parameters Delta m(2) and sin(2)2 theta(v) from the ''conservative'' regions of the MSW solution, derived by taking into account possible relatively large uncertainties in the values of the B-8 and Be-7 neutrino fluxes. Our results show that the one-year-averaged D-N asymmetry in the upsilon(e) survival probability for neutrinos crossing the Earth's core can be, in the case of sin(2)2 theta(v) less than or equal to 0.013, larger than the asymmetry in the probability for (only mantle crossing+core crossing) neutrinos by a factor of up to 6. The enhancement is larger in the case of neutrinos crossing the inner 2/3 of the core. This indicates that the Super-Kamiokande experiment might be able to test the sin(2)2 theta(v) less than or equal to 0.01 region of the MSW solution of the solar neutrino problem by performing selective D-N asymmetry measurements.