  We provide a "first principles" description of scattering from open quantum
systems subject to a Lindblad-type dynamics. In particular we consider the case
that the duration of the scattering process is of similar order as the
decoherence time of the scatterer. Under rather general conditions, the
derivations lead to the the following new result: The irreversible
time-evolution may cause a reduction of the system's transition rate being
effectuated by scattering. This is tantamount to a shortfall of scattering
intensity. The possible connection with striking experimental results of
neutron and electron Compton scattering from protons in condensed matter is
mentioned.
