  We consider the resonant scattering of coherent electromagnetic waves by a
Raman-like process in the gamma ray range off electrostatic modes in a quantum
plasma using a collective Klein-Gordon-Maxwell model. The growth rates for the
most unstable modes are calculated theoretically, and the results are found to
be more efficient than incoherent Compton scattering off individual electrons
above a critical amplitude of the electromagnetic wave. The model does not
predict Raman scattering off pair modes that exist in the Klein-Gordon-Maxwell
model. The results are relevant for coherent gamma rays created in forthcoming
laboratory experiments or in astrophysical objects.
