Rayleigh scattering, elastic photon scattering by bound electrons

New theoretical predictions for the contribution to elastic photon scattering due to the bound atomic electrons are presented which are valid for all shells of all isolated atoms for photon energies 1 keV through 10 MeV. These predictions are based on the direct numerical evaluation of the 2nd order S-matrix following the method of Brown and co-workers as extended by Johnson and co-workers. By comparison of the numerical amplitudes with previous simpler theories, the circumstances for which the form factor approximation and the modified form factor approximation will yield useful predictions for the Rayleigh scattering amplitudes for a given shell and the total atom are summarized. In addition, effects of screening (choice of potential) and relativistic effects are discussed. A prescription for the accurate (0(5%)) prediction of the Rayleigh amplitudes for this photon energy range is described and sample tabulations of the differential scattering amplitudes are presented. These predictions for the Rayleigh amplitudes are used to investigate discrepancies between previous theory and experiment which occur for medium to heavy elements for photon energies 1 to 10 MeV and 10 to 100 keV. At 1.33 MeV, the large-angle disagreement for experiments on lead cannot be resolved; it is concluded that the theoretical calculation of Brown and Mayers is at fault. For 2.75-MeV photons scattered by lead, the theoretical Rayleigh amplitudes predicted by Cornille and Chapdelaine are confirmed, and it is suggested that Coulomb corrections to the Born approximation Delbrueck amplitudes of Papatzacos are responsible for the discrepancies. At 6.84 MeV, estimated that the form factor approximation yields predictions for the L-shell Rayleigh amplitudes which are too large by 15%. For experiments below 100 keV, the form factor approximation is poor particularly for photon energies near the photoeffect K-edge