Implications of CHOOZ results for the decoupling of solar and atmospheric neutrino oscillations

We have considered the results of solar and atmospheric neutrino oscillation experiments in the scheme of mixing of three neutrinos with a mass hierarchy. It is shown that the recent results of the CHOOZ experiment imply that |U_{e3}|^2<<1 (U is the neutrino mixing matrix), that the oscillations of solar neutrinos are described by the two-generation formalism and that the oscillations of solar and atmospheric neutrinos decouple. It is also shown that if not only |U_{e3}|^2<<1 but also |U_{e3}|<<1, then the oscillations of atmospheric neutrinos do not depend on matter effects and are described by the two-generation formalism. In this case, with an appropriate identification of the mixing parameters, the two-generation analyses of solar and atmospheric neutrino data provide direct information on the mixing parameters of three neutrinos. We discuss the possibility to get information on |U_{e3}|^2 in long-baseline neutrino oscillation experiments.