The Scattering of Light by Free Electrons according to Dirac's New Relativistic Dynamics

Abstract

DIRAC and Gordon have given a quantum-dynamical treatment of the problem of the scattering of light by free electrons which seems to be in good agreement with experimental results. Since the development due to Dirac of a more rational relativistic dynamics of the electron, which automatically takes the socalled ‘spin’ phenomena into account, the basis of the theory of the intensity and polarisation of the Compton scattering is, however, somewhat modified. We have undertaken a calculation, based on the new theory, of the intensity of the light scattered by an electron under the influence of a plane monochromatic wave train. When the incident radiation is unpolarised—a case where the least deviation from the former theory would be expected—our result can be expressed by the following formula: Here I is the intensity at the distance r from the electron of the light due to a Compton process, where the secondary light quantum is emitted in a direction forming an angle θ with the incident beam of intensity I₀ and frequency v. Further, e, and m denote charge and mass of the electron, c the velocity of light, and h the Planck constant.