Level crossings in solar-neutrino oscillations

We quantitatively analyze a recently discovered mechanism for the conversion of ${\nu }_e$ into ${\nu }_{\mu }$ from propagation in matter. We derive an approximate analytic solution for adiabatic propagation to calculate solar-neutrino capture rates of ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ and ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ detectors. We use standard solar-model results of the electron density, the neutrino source distribution, and the neutrino-energy spectra. We obtain the implied constraints on oscillation parameters from the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ experiment.