Validity of common assumptions for anomalous scattering

The usual description of Rayleigh scattering (the component of elastic photon-atom scattering identified with scattering from bound electrons) separates the high-energy fixed-momentum-transfer limit (generally taken to be specified in terms of the atomic form factor) from additional contributions to the amplitude, known as anomalous scattering factors or anomalous dispersion corrections. We use explicit results from a full relativistic numerical calculation of Rayleigh scattering to emphasize that several common assumptions regarding these anomalous scattering factors, still mistakenly used although previously criticized, are not entirely appropriate: (1) The anomalous scattering factors should not be identified with the difference from form factor; (2) the imaginary forward scattering factor $f^{\prime \prime }$ is not determined solely from photoeffect at high energy ($\gtrsim 2m{c}^2$); (3) the imaginary forward amplitude includes bound-bound resonance contributions below the photoeffect threshold, which are needed to ensure that the real forward scattering factor obtained from $f^{\prime \prime }$ through a dispersion relation goes to a finite value as the threshold is approached from above; (4) the imaginary anomalous amplitudes do not have the angular dependence of the form factor, but rather a weaker angular dependence, with the consequence that the imaginary amplitude can be comparable in magnitude with the real amplitude at some nonforward angles; and (5) the ratio of parallel and perpendicular anomalous amplitudes is not simply $cos\theta$.