Solar neutrinos and the Mikheyev-Smirnov-Wolfenstein theory

The observation of solar neutrinos by Kamiokande shows that the solar-neutrino problem cannot be solved by changing the solar model. In combination with the observations with a chlorine detector, it makes the nonadiabatic form of the Mikheyev-Smirnov-Wolfenstein theory most likely, and determines Δ${\mathit{m}}^2$ ${\sin }^2$θ=1.0×${10}^{\mathrm{-}8}$ ${\mathrm{eV}}^2$. Probably all neutrinos go through the resonance in the Sun, those from ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ nonadiabatically, all others adiabatically. The latter emerge from the Sun in the higher-mass eigenstate ${\nu }_2$ and have a probability ${\sin }^2$θ to be detected as ${\nu }_{\mathit{e}}$. The gallium experiments, when done with sufficient accuracy, will be able to determine Δ${\mathit{m}}^2$=${\mathit{m}}^2$(${\nu }_{\mathrm{\mu }}$)-${\mathit{m}}^2$(${\nu }_{\mathit{e}}$) within fairly close limits. If the day-night effect can be measured, it will further constrain these limits. The small value of Δ${\mathit{m}}^2$ ${\sin }^2$θ explains why the oscillation from ${\nu }_{\mathit{e}}$ to ${\nu }_{\mathrm{\mu }}$ has not been observed in the laboratory. From existing experiments, the temperature at the center of the Sun can be determined to be within about 6% of that derived from the standard solar model; future neutrino experiments may determine it to within 1%.