  Compton scattering of twisted photons is investigated within a
non-relativistic framework using first-order perturbation theory. We formulate
the problem in the density matrix theory, which enables one to gain new
insights into scattering processes of twisted particles by exploiting the
symmetries of the system. In particular, we analyze how the angular
distribution and polarization of the scattered photons are affected by the
parameters of the initial beam such as the opening angle and the projection of
orbital angular momentum. We present analytical and numerical results for the
angular distribution and the polarization of Compton scattered photons for
initially twisted light and compare them with the standard case of plane-wave
light.
