Mikheyev-Smirnov-Wolfenstein effect in electron-neutrino scattering experiments

We calculate the influence of resonant neutrino scattering [the Mikheyev-Smirnov-Wolfenstein (MSW) effect] in the Sun and in the Earth on measurable quantities in solar-neutrino–electron scattering experiments. The MSW effect reduces the expected rate for ${}_{}{}^8{}_{}{}^{}\mathrm{electron}$ scattering by a factor that ranges from ∼0.8 to ∼0.2 if resonant scattering is the correct explanation for the discrepancy between observation and calculation in the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ experiment. The Earth can produce a significant diurnal effect for certain values of the neutrino mixing angle and mass difference.