Journal of American Science, 2012;8(5) http://www.americanscience.org http://www.americanscience.org editor@americanscience.org 640 The Leptonic , , e e Pair Production in the Photon Interaction with Electromagnetic Field of Light Nuclei S.A. ALkhateeb Department of Mathematics, Science Faculty For Girls, King Abdul-Aziz University, Jeddah , Saudi Arabia sadah_alkhateeb@hotmail.com Abstract: The analytical and numerical calculations for the problem of photoproduction of (lepton-anti lepton)- pairs in the electromagnetic field of light nuclei has been done. applying the obtained formulae for the energy distribution of the pair-production process to the cases of , e e , -pairs in ultra relativistic regions of incident photon energy. and .Comparing the results for the different cases of pair - production , we can show that the cross-sections for the - pair due to the electric and magnetic fields of the target nucleus are larger than that for the e e and - pairs , and that the magnetic field of target nucleus is more effective than the electric field of the nucleus in the , e e , and - pair production processes. We can also show that the values cross-sections of the processes due to the electric quadrupole and magnetic octupole of the target nucleus are larger than the values of the cross- sections due to the electric charge distribution and the magnetic dipole moment of the target nucleus in the three cases of the pair-production processes. [S.A. ALkhateeb. The Leptonic , , e e . Pair Production in the Photon Interaction with Electromagnetic Field of Light Nuclei. J Am Sci 2012;8(5):640-645]. (ISSN: 1545-1003). http://www.americanscience.org . 68 Key words: photoproduction of lepton pairs , lepton pair production in nuclear field. 1. Introduction The theoretical treatment of the process of the e e - pair photoproduction was firstly done in 1934 by Nishina and others [1] and by Bethe and Heitler [2] . In 1936, Jaeget and Hulme [3] shows that the calculations of the cross-section of the pair production process give a good results at high energies of incident photon. Hubbell[4]gives a historical review for the e e - pair production by photons from the prediction of the position e by Dirac in 1928 , to 2006. The cross-section data for e e - pair production by photons was given by Hubbell and Seltzer [5] .The study of and - pair production are given in many works ,e.g. [6-10].In this work we shall examine the process of the photoproduction of , e e , and -pairs in the field of light nuclei , having electric charge distribution, magnetic dipole moment , electric quadrupole moment , and magnetic octupole moment , showing the effect of these electric and magnetic properties of target nucleus on the cross-section of the pair – production processes at high energy regions of incident photons. 2.Formulation of the Problem The Feynman diagrams for the problem of photoproduction of leptonic pairs in the electromagnetic field of nuclei are shown in fig.(1) Where the momentum transferred to the nucleus is p k p q . Ignoring the polarization of lepton and anti-lepton in the producing pair and also the polarization of the incident photon , we have the following formula for the differential cross-section of the process concerning the effects of the electric charge ) ( BH d , the magnetic dipole ) 2 ( M d , the electric quadrupole ) 4 ( E d , and the magnetic octupole moments ) 8 ( M d of the target nucleus: 3 x p k p q 2 x 1 x p k q p 3 x p k p q 2 x 1 x p k p q Fig.1 (2) (1)