  We present a general study of a three neutrino flavour transition model based
on the supersymmetric interactions which violate R-parity. These interactions
induce flavour violating scattering reactions between solar matter and
neutrinos. The model does not contain any vacuum mass or mixing angle for the
first generation neutrino. Instead, the effective mixing in the first
generation is induced via the new interactions. The model provides a natural
interpretation of the atmospheric neutrino anomaly, and is consistent with
reactor experiments. We determine all R-parity violating couplings which can
contribute to the effective neutrino oscillations, and summarize the present
laboratory bounds. Independent of the specific nature of the (supersymmetric)
flavour violating model, the experimental data on the solar neutrino rates and
the recoil electron energy spectrum are inconsistent with the theoretical
predictions. The confidence level of the $\chi^2$-analysis ranges between $\sim
10^{-4}$ and $\sim 10^{-3}$. The incompatibility, is due to the new SNO
results, and excludes the present model. We conclude that a non-vanishing
vacuum mixing angle for the first generation neutrino is necessary in our
model. We expect this also to apply to the solutions based on other flavour
violating interactions having constraints of the same order of magnitude.
