  We consider the decoherence effects in the propagation of active neutrinos
due to the non-forward neutrino scattering processes in a matter background
composed of electrons and nucleons. We calculate the contribution to the
imaginary part of the neutrino self-energy arising from such processes. Since
the initial neutrino state is depleted but does not actually disappear (the
initial neutrino transitions into a neutrino of a different flavor but does not
decay) those processes should be associated with decoherence effects that
cannot be described in terms of the coherent evolution of the state vector.
Based on the formalism developed in our previous work for treating the
non-forward scattering processes using the notion of the stochastic evolution
of the state, we identify the jump operators, as used in the context of the
master or Lindblad equation, in terms of the results of the the calculation of
the non-forward neutrino scattering contribution to the imaginary part of the
neutrino self-energy. As a guide to estimating the decoherence effects in
situations of practical interest we give explicit formulas for the decoherence
terms for different background conditions, and point out some of the salient
features in particular the neutrino energy dependence. To establish contact wih
previous works in which the decoherence terms are treated as phenomenological
parameters, we consider the solution to the evolution equation in the
two-generation case. We give formulas that are useful for estimating the
effects of the decoherence terms under various conditions and environments,
including the typical conditions applicable to long baseline experiments, where
matter effects are important. In those contexts the effects appear to be small,
and indicative that if significant decoherence effects were to be found they
would be due to non-standard contributions to the decoherence terms.
