The mixing angles in matter for three generations of neutrinos and the MSW mechanism

Mikheyev and Smirnov have recently shown that oscillations between two species of neutrinos may be amplified in matter. We give analytic expressions for the energy eigenvalues, all the mixing angles and the CP-violating phase in matter for three generations of neutrinos using the Fritzsch parametrization for the flavor mixing matrix. For clearly separated neutrino masses Δm 31 2 ≫Δm 21 2 we find two MSW resonance effects—one forv e ↔v µ and one forv e ↔vτ conversions —which can each be approximated by a separate two neutrino treatment as has been recently shown by Kuo and Pantaleone. Nearly degenerate neutrino masses Δm 31 2 ∼Δm 21 2 on the other hand lead to only one resonance region withs 1 2 m 2 no longer necessarily approaching 1 for very high densities.