ONE LOOP VACUUM POLARIZATION CONTRIBUTION TO THE RADIATIVE CORRECTION TO THE SCATTERING OF ELECTRON BY COULOMB POTENTIAL

Abstract

The main purpose of this study is to provide the quantum description for the Vacuum polarization contribution to the radiative correction 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 vacuum polarization. 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 vacuum polarization and total differential cross section using Fermi Golden rule. The Numerical result for the differential cross-section have been generated by using matlab for plot the graph. Finally compare the next to leading order and total differential cross sections with that of the leading order differential cross section. 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. This is the validation of perturbation theory.