RELATIVISTIC DESCRIPTION OF ELECTRON-MUON SCATTERING REACTION

Abstract

In this thesis, detailed derivations of the spin-average invariant amplitude and hence the differential cross-section for unpolarized electron-muon elastic scattering are made by using lowest-order Feynman diagrams. It has taken electron and muon of a spin-

which allows a consistent quantum electrodynamical description of the scattering process. The Feynman rules, Casimir’s trick and trace theorems have been employed in constructing the relativistic expression of spin-average invariant amplitude. Moreover, by integrating over the Dirac-delta function it shows the dependence of differential cross section on the energy and scattering angle of the final state. Furthermore, the final result of the equation of differential cross section is converted to the Fortran 95 code, and from the results; the graph of unpolarized differential cross section against scattering angles is plotted by using Origin Pro7.0. Numerical result of the differential cross section for electron-muon elastic scattering in lab frame is maximum at forward angles and levels off as the angle increases. Moreover, negligible contribution comes from incident energy above 100MeV to the angular distribution. The result is also much consistent with the Mott predictions at forward angles and low incident energy of electron.