Analytical treatment of high transcendental functions involved in perturbation theory for inner shell electrons interaction with gamma-ray

摘要

This paper presents new analytical and numerical methods for handling the Appell and Gauss Hypergeometric functions involved in the relativistic elastic two photon scattering by inner shell electrons and in photoeffect and pair production processes. We find a possibility to reduce the number of needed Appell functions using their specific structure via recursion relationships. The oscillating nature of the integrand of the Appell functions in the high energy regime specific to γ-ray scattering is investigated and the solution for their accurate calculation on standard computer facilities is shown. The numerical results obtained using the presented methods were compared with other's authors results, displaying a very good agreement.