JKAU: Sci., Vol. 23 No. 2, pp: 65-78 (2011 A.D./1432 A.H.) DOI: 10.4197 / Sci. 23-2.5 65 Polarization Dependence of the Bremsstrahlung Cross- Section in the Scattering of Electrons by Nuclei with Electromagnetic Multipole Moments S. A. Al-Khateeb Department of Mathematics, Faculty of Science for Girls, King Abdulaziz University, Jeddah, Saaudi Arabi Abstract. The present work deals with one of the most important problem in the quantum electrodynamics, 1.e the problem of bremsstrahlung process due to the interaction between lepton (electron) and the field of nuclei having electromagnetic multipole distributions. The detaild calculations for the cross-sections and the angular and energy distributions of the process are given in the first Born approximation of the quantum perturbation theory in two cases: With neglecting the polarizations of the photon and the electron, and with studying these polarizations. Applying the obtained formulae to some nuclei, the light nucleus ( ) 9 4 Be and the heavier one ( ) 27 13 Al , to showing the effect of both circular photon polarization and longitudinal electron polarization on the bremsstahlung cross-section, and comparing the results obtained for the two nuclei graphically. I-Introduction The Study of the bremsstrahlung process was firstly done by Bethe and Heitler [1] in 1934, and many works about this process could have appeared in the period (1934-1954) [2-4] . In these works, the polarizations of the photons of bremsstrahlung and of the electrons were not studied because of the complicity of the calculations in this case.The circular polarization of bremsstrahlung photons due to the collision of longitudinally polarized electrons with nuclei, was firstly investigated by Grodzins [5] in 1959. At the same time, Olsen and Maximon [6] studied the circular polarization of the bremsstrahlung photons experimentally. Motz