The Transition from Ordinary Dispersion into Compton Effect

Abstract

THE dispersion formula of Kramers and Heisenberg is valid for an atomic system the dimensions of which are small compared with the wave-length of incident light. For very short waves the scattering from an atom will of course approach the Compton effect for free electrons; and this has been treated very fully by Dirac and Gordon. A treatment of dispersion theory on the basis of wave mechanics has been given by Schrödinger and Klein, who have also outlined a simple treatment of the Compton effect. Following a procedure rather analogous to that of Klein, it is possible to work out a generalised dispersion formula, holding also for waves short compared with atomic dimensions and making it possible to follow the gradual transformation of ordinary dispersion into the Compton effect.