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Three neutrino flavors: Oscillations, mixing, and the solar-neutrino problem.

An analytical, quantitative description of solar-neutrino propagation is presented which includes three flavors, matter dependence, and long-wavelength effects. Using the derived expression for the electron-neutrino survival probability, it is demonstrated that mixing is possible between the two-flavor Mikheyev-Smirnov-Wolfenstein and two-flavor long-wavelength solutions to the solar-neutrino problem. However, adiabatic conversion of a neutrino mass eigenstate tends to suppress all subsequent long-wavelength effects such as seasonal'' variations in the solar-neutrino flux.