Validity of nonrelativistic dipole approximation for forward Rayleigh scattering

The validity of nonrelativistic dipole approximation (NRDPA) in predicting forward Rayleigh scattering amplitudes is examined. Gavrila's analytic Coulomb $K$-shell amplitudes are compared with the results of a relativistic numerical calculation based on a multipole expansion of the second-order $S$-matrix element. The real part of the forward amplitude is predicted fairly well in NRDPA at all energies, including the low-energy regime where form-factor approximation fails. The imaginary part of the amplitude is fairly well predicted by NRDPA not too far above threshold, but the prediction fails at higher energies. The dipole contribution to these amplitudes is dominant below and near threshold, but higher multipoles become increasingly important at higher photon energies. The continued usefulness of NRDPA provides another illustration of the cancellation among relativistic, retardation, and higher multipole contributions.