Class of models leading to depletions of solarνeand atmosphericνμfluxes

A model incorporating three left-handed ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L\times {\mathrm{U}\mathrm{}\left(1\right)\mathrm{}}_Y$ doublet neutrinos and three right-handed singlet neutrinos, with leptonic Dirac mass submatrices similar to empirical forms which work well for quarks, is required to yield both the nonadiabatic Mikheyev-Smirnov-Wolfenstein solar neutrino effect and the depleted flux of atmospheric muon neutrinos observed by Kamiokande. We find a small segment of the ${\delta m}_{23}^2$ vs ${sin}^2{2\theta }_{23}$ plane exists where such solutions can be achieved and identify the class of right-handed Majorana submatrices required.