VERTEX CORRECTION AND SOFT PHOTON EMISSION CONTRIBUTIONS TO THE SCATTERING OF ELECTRON BY COULOMB POTENTIAL

Abstract

The main purpose of this study is to provide the quantum description for the vertex correction and soft photon emission contributions to the radiative corrections of the scattering of electron by coulomb potential. Using Feynman rules of quantum electrodynamics (QED), we evaluate the leading order scattering matrix from the lowest order Feynman diagram, the next to leading order scattering matrix from the higher order Feynman diagram for the scattering of electron by Coulomb field in the case of vertex correction and also evaluate the scattering matrix for the scattering of electron by Coulomb field with soft photon emission. Next, we evaluate the square of the scattering matrix using Cashimer’s trick and calculate the leading order differential cross section, the next to leading order differential cross sections in the case of vertex correction and soft photon emission and total differential cross section using Fermi Golden rule. Finally compare the next to leading order and total differential cross sections with that of the leading order differential cross section. Of course, the next to leading order differential cross section is very small compared with the leading order differential cross section and the total cross section is comparable with that of the leading order differential cross section. These are of course valid in perturbation theory.