The total cross-sections for the photoeffect for K-shell bound electrons and pair production with the created electron in the ground state for photon energies above 1 MeV

Abstract

Considering the contributions of the main term of the relativistic Coulombian Green function given by Hostler to the second order of S matrix element and taking into account only the large components of the Dirac spinor of the ground state we obtain the imaginary part of the Rayleigh amplitudes in terms of elementary functions. Thereby simple and high accurate formulae for the total cross-sections for photoeffect and pair production with the electron created in the K-shell are obtained \textit{via} the optical theorem.Comparing the predictions given by our formulae with the full relativistic numerical calculations of Kissel \textit{et al} [Phys. Rev. A 22, 1970 (1980)] and Scofield [LLRL, Internal Report,1973], a good agreement is found for photon energies above the pair production threshold up to 5 MeV for any Z elements. We present our numerical results for the total photoeffect and pair production cross-sections, for various photon energies for the K-shell of Ag and Pb.