Rayleigh scattering by neutral atoms, 100 eV to 10 MeV

We calculate the contribution to elastic photon scattering from an atom due to scattering off the bound atomic electrons (Rayleigh scattering). We compare predictions resulting from our numerical evaluation of the relativistic second-order $S$ matrix in a screened central potential with other theories, particularly the form-factor approximation. We give a prescription for accurate $O(1\%)\mathrm{}$ evaluation of total-atom Rayleigh amplitudes (summed over electrons) and present sample tabulations for lead ($Z=82\mathrm{}$) for energies of experimental interest in the range from 22.1 to 2750 keV. Based on our prescription we compare elastic-scattering cross sections using Rayleigh amplitudes with selected experiments and are able to remove the large factor-of-two discrepancies previously reported.