Decoupling of solar and atmospheric neutrino oscillations

The scheme of mixing of three neutrinos with a mass hierarchy is considered for the explanation of the solar and atmospheric neutrino problems through neutrino oscillations. It is shown that the recent results of the CHOOZ experiment imply that the element U_{e3} of the neutrino mixing matrix is small, that the oscillations of solar neutrinos are described by the two-generation formalism and that the oscillations of solar and atmospheric neutrinos decouple. Furthermore, if |U_{e3}|<