The phenomenon of neutrinos changing flavor as they propagate through matter is examined with three neutrino flavors. For the important case of small mixing angles and/or well-separated mass scales, the three-neutrino problem is well approximated by two resonances occurring at different densities. An analytic expression for the oscillation probability is obtained which is valid for large mixings. It is applied to the solar-neutrino problem, both analytically and in terms of detailed, numerical calculations. For three flavors there are four parameters in the problem, as compared with two parameters in the two-flavor approximation. Planned experiments which are sensitive to the flavor dependence of the neutrino spectrum could determine these four parameters.

• Received 29 December 1986

DOI:https://doi.org/10.1103/PhysRevD.35.3432