Mixed MSW and Vacuum Solutions of Solar Neutrino Problem

Assuming three flavour neutrino mixing takes place in vacuum, we investigate the possibility that the solar $\nu_e$ take part in MSW transitions in the Sun due to $\Delta m^2_{31} \sim (10^{-7} - 10^{-4})~eV^2$, followed by long wave length vacuum oscillations on the way to the Earth, triggered by $\Delta m^2_{21}$ (or $\Delta m^2_{32}$) $\sim (10^{-12} - 10^{-10})~eV^2$. The solar $\nu_e$ survival probability is shown to be described in this case by a simple analytic expression. New ranges of neutrino parameters which allow to fit the solar neutrino data have been found. The best fit characterized by the minimum $\chi^2$ is extremely good. This hybrid (MSW+vacuum oscillations) solution of the solar neutrino problem leads to peculiar distortions of energy spectrum of the boron neutrinos which can be observed by the SuperKamiokande and SNO experiments. Other flavour scheme (e.g. 2 active $\nu$s + 1 sterile $\nu$) can provide MSW+vacuum solution also.