Relationship of the relativistic Compton cross section to the electron's velocity distribution

Abstract

A relativistic treatment of the Compton cross section for free electrons is given. In addition, conditions are specified when it is correct to within 1% to relate in a simple manner the results of Compton-scattering experiments to a simple Compton profile (velocity distribution of electrons). Many different approaches previously used to achieve this simple relationship have been arbitrary and thus have resulted in the possibility that two investigators with the same experimental data would deduce different Compton profiles. The relationship derived here differs from all the previous ones, and in some cases, would yield a significantly different Compton profile from reported data.