Scattering of Radiation by Electrons in Relativistic Quantum Mechanics

Abstract

The theory of the scattering of radiation by Dirac electrons is revised and extended. Assuming negative energy states unoccupied, a formula for the cross section of coherent scattering of very hard quanta is derived. It is, furthermore, shown that the previously claimed and accepted one-to-one correspondence of the matrix elements for the cases of free or occupied negative energy states is generally untrue. It can be proved that for moderately small quanta the cross sections of coherent and incoherent scattering by bound electrons are approximately the same in the case of unoccupied negative energy states and in the pair theory proper. Characteristic differences are shown to exist for very hard radiation. The historical development of the problems here treated is also discussed.