  We consider the decoherence effects in the propagation of neutrinos in a
background composed of a scalar particle and a fermion due to the non-forward
neutrino scattering processes. Using a simple model for the coupling of the
form $\bar f_R\nu_L\phi$ we calculate the contribution to the imaginary part of
the neutrino self-energy arising from the non-forward neutrino scattering
processes in such backgrounds, from which the damping terms are determined. In
the case we are considering, in which 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 into a $f\phi$ pair, for
example), we associate the damping terms with decoherence effects. For this
purpose we give a precise prescription to identify the decoherence terms, as
used in the context of the master or Linblad equation, in terms of the damping
terms we have obtained from the calculation of the imaginary part of the
neutrino self-energy from the non-forward neutrino scattering processes. The
results can be directly useful in the context of Dark Matter-neutrino
interaction models in which the scalar and/or fermion constitute the
dark-matter, and can also serve to guide the generalizations to other models
and/or situations in which the decoherence effects in the propagation of
neutrinos originate from the non-forward scattering processes may be important.
As a guide to estimating such decoherence effects, the contributions to the
absorptive part of the self-energy and the corresponding damping terms are
computed explicitly in the context of the model we consider, for several
limiting cases of the momentum distribution functions of the background
particles.
