Analytic treatments of matter-enhanced solar-neutrino oscillations

Mikheyev and Smirnov have pointed out that flavor oscillations of solar neutrinos could be greatly enhanced. The Mikheyev-Smirnov-Wolfenstein mechanism depends on the effective electron neutrino mass that arises from charged-current scattering off solar electrons, a phenomenon first discussed by Wolfenstein. Two analytic treatments, the adiabatic approximation and Landau-Zener (LZ) approximation, have been used in studies of this mechanism. I discuss a simple extension of the LZ approximation that merges naturally with the adiabatic approximation and is free of certain troublesome pathologies that arise in the conventional treatment. In this extension the solar density is approximated as in the conventional treatment, except that the starting and ending densities are the physical ones. Results of this finite LZ approximation are compared to those from the standard LZ approximation, the adiabatic approximation, and ``exact'' numerical integrations. The new approximation is virtually exact regardless of the point of origin of the neutrino in the solar core. This approximation is used to efficiently calculate the solar-neutrino capture rates for ³⁷Cl, ⁷¹Ga, and ⁹⁸Mo. The spatial extent of the solar core, the contributions of minor neutrino species, and the effects of ⁸B neutrino capture to excited nuclear states are treated with care. Limits imposed on {δ}m² and sin²2thetaᵥ by the nonzero ³⁷Cl capture rate are derived by considering the expected uncertainties in standard-solar-model flux estimates. Those oscillation parameters are determined that could account for the ³⁷Cl puzzle and yet lead to a ⁷¹Ga counting rate above the minimum astronomical value. I determine, in the event that such an ambiguous result arises, the extended region of the {δ}m²-sin²2thetaᵥ plane that would be ruled out. The possibility that the ⁸B neutrino capture cross section for ³⁷Cl may be slightly larger than the conventional value is briefly discussed.