ATMOSPHERIC NEUTRINOS WITH 3-FLAVOR MIXING

We analyze the atmospheric neutrino data in the context of three flavo r neutrino oscillations taking account of the matter effects in the Ea rth. With the hierarchy among the vacuum mass eigenvalues mu(3)(2) muc h greater than mu(2)(2) greater than or equal to mu(1)(2), the solutio n of the atmospheric neutrino problem depends on delta(31) = mu(3)(2) - mu(1)(2) and the 13 and 23 mixing angles phi and psi. Whereas the su b-GeV atmospheric neutrino data imposes only a lower limit on delta(31 )>10(-3)eV(2), the zenith-angle-dependent suppression observed in the multi-GeV data limits delta(31) from above also. The allowed regions o f the parameter space are strongly constrained by the multi-GeV data. Combined with our earlier solution to the solar neutrino problem which depends on delta(21) = mu(2)(2) - mu(1)(2) and the 12 and 13 mixing a ngles omega and phi, we have obtained the ranges of values of the five neutrino parameters which solve both the solar and the atmospheric ne utrino problems simultaneously.