  We are looking at a Dirac electron in the electromagnetic field of a plane
monochrome polarized X-ray. It will be attempted to link the terms of a certain
(joint) asymptotic expansion of the Heisenberg propagations of momentum- and
total-energy- observables with collision of the electron with 1, 2, 3, photons.
Our asymptotic expansion neglects terms small for states of very high
frequencies, and might be natural, in many respects. A special focus will be
given to the single collision term. We attempt a description of this term as a
(distribution) integral operator, to analyze directionally different
oscillations of the electron, to be compared with those of the Compton model.
We obtain agreement of scattering frequencies, but not of scattering
directions. It might be recalled, in that respect, that the Dirac particle is
not a simple mass point - it has a dual nature as electron-positron; it has a
spin who possibly could rotate after the collision, then absorbing
energy-momentum, etc.
