Implication of gallium results on the possibility of observing day-night matter oscillations at SNO, Super-Kamiokande, and Borexino

Calculations are presented to determine what real time day-night effects would be observable at SNO, Super-Kamiokande, or Borexino for the Δ${\mathit{m}}^2$, ${\sin }^2$2θ space allowed by the present gallium, ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$, and Kamiokande solar neutrino results. We show that the combination of possible day-night effects and the observation of overall neutrino detection rates in the upcoming experiments might allow discrimination between the allowed regions of mass and mixing parameters. Approximate analytical expressions for the real time MSW effect in the Earth are presented to clarify the nature of electron-neutrino regeneration as a function of path length through the Earth. We point out that even for the allowed small ${\sin }^2$2θ MSW solution, it might be possible to detect a day-night effect for neutrino trajectories through the core of the Earth.