Solar and atmospheric neutrinos in three generations with a magnetic moment

A solution to the solar and atomospheric neutrino problems in three generations in the joint context of matter oscillations and the magnetic moment is investigated. An appropriate rotation of the evolution Hamiltonian reduces the three generation case to a two generation one. A convenient background for such a scenario with small neutrino masses and large magnetic moments is given by the Zee-type models, in which the mass generation mechanism leads to a pair of separate orders of magnitude for the mass square differences between neutrino species. We obtain a ratio ɛ≃${10}^{\mathrm{-}2}$–${10}^{\mathrm{-}3}$ between these orders of magnitude, so that one of them [(0.3–3)×${10}^{\mathrm{-}2}$ ${\mathrm{eV}}^2$] is suitable for the atmospheric neutrino solution and the other (∼${10}^{\mathrm{-}5}$ ${\mathrm{eV}}^2$) for the solar neutrino solution. The magnetic moment leads to a decrease of the survival probability with solar neutrino energy. Such a decrease is consistent with the experimental situation.