Elastic photon scattering at small momentum transfer and validity of form-factor theories

Various form-factor theories used to predict Rayleigh-scattering cross sections of gamma-ray photons are examined. For energies above the $K$ threshold comparisons are made with more accurate numerical calculations, for a high-$Z$ element (Pb), primarily at small momentum transfers [up to $x\equiv {\lambda }^{-1\mathrm{}}sin\left(\frac{\theta }{2}\right)=10\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, where $\lambda$ is the photon wave-length] but also for larger momentum transfers. Nonrelativistic form-factor predictions generally are in good agreement with the numerically obtained theoretical values, in contrast to poorer predictions obtained with relativistic form factors. However, we also observe that a modified relativistic form-factor theory predicts the theoretical Rayleigh-scattering amplitudes still more accurately, to higher momentum transfers. Comparison with available experiments for Pb at energies from 145 to 1408 keV and momentum transfers $x\le 10$ ${\mathrm{\AA }}^{-1\mathrm{}}$ indicates no systematic pattern of discrepancy between theory and the significant scatter among different experimental results.