Elastic scattering of X-rays and gamma rays by 2S electrons in ions and neutral atoms

The nonrelativistic limit of Rayleigh scattering amplitude on 2s electrons of neutral and partially ionized atoms is obtained by making use of the Green Function method. The result takes into consideration the retardation, relativistic kinematics and screening effects. The spurious singularities introduced by the retardation in a nonrelativistic approach are cancelled by the relativistic kinematics. For neutral and partially ionized atoms, a screening model is considered with an effective charge obtained by fitting the Hartree-Fock charge distribution with pure Coulombian wave functions corresponding to a central potential of a nucleus with Z_eff as the atomic number. The total cross section of the photoeffect on the 2s electrons is also calculated from the imaginary part of the forward scattering amplitude by means of the optical theorem. The numerical results obtained are in a good agreement (10%) with the ones obtained by Kissell for the Rayleigh amplitude and by Scofield for the Photoeffect total cross section on the 2s electrons, for atoms with atomic number 18 ≤ Z ≤ 92 and photon energies $ω≤αZm$⁠. (α=1/137,... is the fine structure constant, m is the electron mass).