The Dirac Equation of the Compton Effect

TL;DR

This paper explores the Dirac equation in the context of the Compton effect, linking asymptotic expansions of quantum propagators with electron-photon collisions, and analyzing scattering frequencies and directions.

Contribution

It introduces a novel asymptotic expansion approach to describe electron-photon interactions within the Dirac framework, focusing on single collision terms and their oscillatory behavior.

Findings

Agreement in scattering frequencies with the Compton model

Discrepancy in scattering directions compared to classical predictions

Analysis of electron oscillations post-collision

Abstract

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.