SOLAR AND ATMOSPHERIC NEUTRINO OSCILLATIONS WITH 3 FLAVORS

We analyze the solar and the atmospheric neutrino problems in the cont ext of three flavor neutrino oscillations. We assume a mass hierarchy in the vacuum mass eigenvalues mu(3)(2) much greater than mu(2)(2) gre ater than or equal to mu(1)(2), but make no approximation regarding th e magnitudes of the mixing angles. We find that there are small but co ntinuous bands in the parameter space where the constraints imposed by the current measurements of Ga-71, Cl-37, and Kamiokande experiments are satisfied at the la level. The allowed parameter space increases d ramatically if the error bars are enlarged to 1.6 sigma. The electron neutrino survival probability has a different energy dependence in dif ferent regions of the parameter space. Measurement of the recoil elect ron energy spectrum in detectors that use v-e scattering may distingui sh between some of the allowed regions of parameter space. Finally we use the results for the parameter space admitted by the solar neutrino s as an input for the atmospheric neutrino problem and show that there exists a substantial region of parameter space in which both problems can be solved.