ELECTRON-POSITRON PAIR PRODUCTION FROM PHOTON IN THE PRESENCE OF NUCLEI

Abstract

We have employed the Covariant Perturbation Theory and Feynman rules to calculate the transition probability to the process of electron- positron pair production from photon in the field of atomic nuclei. The traces of matrices in the transition probability and the differential cross section have been evaluated for pair production in the field of nuclei. The main purpose of this study was calculating the cross–section of the electron positron pair production from photon in the presence of nuclei with charge. This work was focus the determination of scattering amplitude, transition probability and scattering cross section for electron-positron pair production by an incoming photon in the presence of nuclei. The interaction picture is useful in dealing with changes to the wave functions and observables due to interactions. The interaction picture is a special case of unitary transformation applied to the Hamiltonian and state vectors. For our purpose we are interested in calculating the average transition probability per unit space-time volume. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. Electrons and positrons Pairs can be produced if a photon interacts with the nucleus of an atom. This process is related by some symmetry to the production of Bremsstrahlung photons. Going from bremsstrahlung to pair production, we see that the outgoing photon becomes an ingoing photon and the ingoing negation becomes an outgoing positron. We have seen that the pairs of electrons and positrons can be produced if a photon interacts with the nucleus of an atom. Pair production has to happen near a nucleus so that both energy and momentum can be conserved. For photons with high photon energy (MeV scale and higher), pair production is the dominant mode of photon interaction with matter.