Rayleigh scattering of x-ray and γ-ray by 1s and 2s electrons in ions and neutral atoms

Abstract

Using the Coulomb–Green function method and considering the nonrelativistic limit for the two-photon S-matrix element, the right nonrelativistic 2s Rayleigh scattering amplitudes are obtained. Our result takes into account all multipoles, retardation and relativistic kinematics contributions, and the old dipole approximation result of Costescu [1] is retrieved as a limit case. The total photoeffect cross-section which is related to the imaginary part of the Rayleigh forward scattering amplitude through the optical theorem is also obtained. Our Coulombian formulae are used in the more realistic case of elastic scattering of photons by bound 1s and 2s electrons in ions and neutral atoms. Screening effects are considered in the independent particle approximation through the Hartree–Fock method. The effective charge Zeff is obtained by fitting the Hartree–Fock charge distribution by a Coulombian one. Good agreement (within 10%) is found when comparing the numerical predictions given by our nonrelativistic formulae with the full relativistic numerical results of Kissel [2] in the case of elastic scattering of photons by 1s and 2s electrons and Scofield [3] in the case of K-shell and 2s subshell photoionization for neutral atoms with 18 ⩽ Z ⩽ 92 and photon energies ω ⩽ αZm.