ORIGINAL PAPER Relativistic elastic scattering of hydrogen atoms by positron impact with anomalous magnetic moment effects E Hrour , M El Idrissi , S Taj and B Manaut* Laboratoire Interdisciplinaire de Recherche en Sciences et Techniques, Faculte´ Polydisciplinaire, Universite´ Sultan Moulay Slimane, Boite Postale 523, 23000 Be´ni Mellal, Morocco Received: 30 October 2014 / Accepted: 16 December 2014 Abstract: Elastic scattering of hydrogen atoms by positron impact is studied at various values of incident positron energy and laser intensities. A discussion of differential cross-sections for positron scattering by hydrogen atoms in presence of laser field is presented along with anomalous magnetic moment of both electrons and positrons fully included. Differential cross sections for electrons and positrons remain almost equal in absence of anomalous magnetic moment effects. A comparison is also made with introduction of anomalous magnetic moment effects of both electrons and positrons. At intensities equal to 0.05 a.u. and above significant discrepancies in differential cross section is found even in first Born approximation. Keywords: Laser assisted; QED calculations; AMM effects; Relativistic scattering theory PACS Nos.: 34.80.Dp 1. Introduction Scattering of electrons and positrons by hydrogen atoms is a most fundamental process in relativistic atomic colli- sions. Since hydrogen is only atom for which, non rela- tivistic and relativistic wave functions are known exactly, relativistic e  H collision processes including relativistic effects provide an attractive testing ground for scattering theories in quantum electrodynamics (QED). Most precise and specific tests of QED consist of measurements of electromagnetic fine structure constant a, which is pro- portional to anomalous magnetic moment. At the zeroth order of perturbation, QED predicts that g is equal to 2 for an electron and a positron. Interaction of an electron (or a positron) with vacuum, as described by QED, yields a value of g for an electron (or a positron) that is slightly greater than 2 by roughly one part-per-thousand. This deviation from 2 is called anomalous magnetic moment, a e  , defined by g=2 ¼ 1 þ a e  . A measurement of electron g-value provides a precise test of Dirac theory and QED. For almost 20 years, best measured value of anomalous magnetic moment for free electron is [1, 2] a e  ¼ 0:00115965218073ð28Þ: For free positron and according to the most accurate demonstration of charged particle–antiparticle symmetry g e  =g e þ ¼ 1 þð0:5  2:1Þ 10 12 , is a e þ ¼ 0:00115965218068ð28Þ: Interaction of antimatter with matter is an interesting and active field of research [3–6]. One of simplest of these types of interactions is between positron–atom [7–12] and posi- tron–molecule [13, 14]. Such interactions are important in atomic and molecular physics. A seminal book ‘‘Positron physics’’ by Charlton and Humberston [15] has given the main advances in the field of positron physics. It addresses a comprehensive account of the field of low energy positron and positronium within atomic and molecular physics. Availability of intense mono-energetic positron beams and recent improvements in measurement techniques now rou- tinely provide new evidence on such topics as Ps formation or positron annihilation and scattering. At first, this paper sets basics of theory needed for such a comparison between Differential Cross Sections (DCSs) of positron and electron, enouncing frame in which, relativ- istic positron theory has been built in. Then, we have dis- cussed Dirac equation for positron, in absence and presence of Anomalous Magnetic Moment (AMM) effects. This is *Corresponding author, E-mail: b.manaut@usms.ma Indian J Phys DOI 10.1007/s12648-015-0649-0 Ó 2015 IACS