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.
