A Study of the Day - Night Effect for the Super - Kamiokande Detector: I. 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 MSW ${\nu }_e\to \text{numt}$ transition solution of the solar neutrino problem. The one-year averaged probability of survival of the solar $\text{nue}$ crossing the Earth 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 (EOA) to describe the Earth 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 $\mathrm{\Delta }{m}^2$ and $si{n}^{2}2{\theta }_V$ from the ``conservative’’ regions of the MSW solution, derived by taking into account possible relatively large uncertainties in the values of the ${}^8$B and ${}^7$Be neutrino fluxes. Our results show that the one-year averaged D-N asymmetry in the ${\nu }_e$ survival probability for neutrinos crossing the Earth core can be, in the case of $sin^22 \theta_{V} \leq 0.13$, larger than the asymmetry in the probability for (only mantle crossing + core crossing) neutrinos by a factor of up to six. 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 $si{n}^{2}2{\theta }_V\le 0.01$ region of the MSW solution of the solar neutrino problem by performing selective D-N asymmetry measurements.