  We present a theory of neutrino oscillations in a dense medium which goes
beyond the effective matter potential used in the description of the MSW
effect. We show how the purity of the neutrino state is degraded by neutrino
interactions with the environment and how neutrino--matter interactions can be
a source of decoherence. We present new oscillation formulae for neutrinos
interacting with leptons and carry out a numerical analysis which exhibits
deviations from the MSW formulae for propagation through the Earth of
ultra-high energy neutrinos. In particular, we show that at high density and/or
high neutrino energy, the vanishing transition probabilities derived for MSW
effect, are non zero when the scattering is taken into account.
