Signatures of the differential Klein‐Nishina electronic cross section in Compton's quantum theory of scattering of radiation

Here, we consider the problem of separating the relative contributions of kinematics and dynamics to the differential Klein‐Nishina electronic cross section using graphical and numerical analysis. We show that the values of the energy of scattered photons, and hence the kinetic energy of recoiled electrons calculated from Compton's quantum theory of scattering of radiation, show a degree of matching that increases with the increase in incident photon energy as quantified by chi-square goodness of fit test, with the calculated differential Klein‐Nishina electronic cross section per electron per unit solid angle for the scattering of an unpolarized photon by a stationary free electron, when appropriate normalization procedures are invoked. There is a high degree of matching in a regime where the total electronic Klein‐Nishina cross section for the Compton scattering on a free stationary electron scales as the inverse of the incident photon energy and the contribution of the electro-magnetic interaction to differential electronic cross section diminishes. Hence the third level explanation of Compton effect by quantum electrodynamics has a degree of matching with the first level of Compton's quantum theory. The degree of mismatch is an indicator of the relative contribution of dynamics to differential Klein‐Nishina electronic cross section compared to kinematics. For incident photon energies less than 1 MeV, we obtain the values of the scattering angles at which calculated differential cross section is nonzero but is kinematically limited which may lead to broadening of Compton profile. At the scattering angle where the differential cross section value is minimum for a given incident photon energy, we obtain the relative contribution of dynamics to the differential cross section compared to kinematics. Therefore, these predictions which need to be confirmed experimentally have significance to the understanding of the mechanisms of photon‐electron interactions in the Compton scattering.