Eur. Phys. J. Plus (2016) 131: 364
https://doi.org/10.1140/epjp/i2016-16364-3

Regular Article

Calculation of the covariant matrix elements, and cross-sections of Compton diffusion on a bound electron

Department of Physics and Astronomy, College of Science, King Saud University, 11451, Riyadh, Saudi Arabia

^* e-mail: salwams@ksu.edu.sa

Received: 1 August 2016
Accepted: 20 September 2016
Published online: 19 October 2016

Abstract

This paper completes a previous published work that calculated analytically the relativistic wavefunctions for bound electron in a Compton diffusion process. This work calculates the relativistic propagator and the Wronskian of the two associated Feynman diagrams of Compton diffusion (emission first and absorption first). Then find an explicit expression for the covariant matrix elements separated into two parts: spin-angular part and radial part. Using these explicit expressions, the effective cross-section for Compton diffusion in the most general form is obtained in terms of basic dynamical and static quantities, like electron’s and photon’s 4-momenta and atomic number. The form of the cross-section is put ready for numerical calculations.