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

The Dirac Equation of the Compton Effect