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

摘要

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