RETARDATION AND MULTIPOLE EFFECTS IN RAYLEIGH-SCATTERING BY HYDROGENLIKE IONS AT LOW AND X-RAY PHOTON ENERGIES

We investigate analytically multipole and retardation effects on Rayleigh scattering of photons from the ground state of a hydrogenic atom. Our approach, which goes beyond the usual form-factor approximation, simplifies the full nonrelativistic point-Coulombic amplitude considerably. We are able to express this simplified full multipole, fully retarded result as simple corrections to the nonrelativistic dipole amplitude. We demonstrate that these corrections are important, and larger than relativistic effects, for photon energies near the K-shell photoionization threshold. They are essential for accurately determining the angular distribution of scattered photons in this regime. We present numerical comparisons with relativistic S-matrix calculations that confirm the validity of our approach in this region for elements of low to moderate nuclear charge. For photon energies well above the K-shell threshold we show that retardation corrections are adequately given by the form factor, which has a greater variation with angles than the anomalous scattering factors. For still higher energies, we demonstrate that the full nonrelativistic result fails due to spurious poles in the imaginary part of the amplitude.