The 'anomalous' dispersion corrections, which are not in fact anomalous, take into account the effect of absorption in the scattering of phonons by electrons. In the classic picture the electron is approximated by a damped harmonic oscillator. The scattering factor of the electron is then complex and the atomic scattering factor, or atomic form factor, is given by:
f + f' + i f"
where f' and f" are the real and imaginary parts of the anomalous dispersion correction. Their importance increases as one gets closer to an absorption edge (resonant scattering). Numerical calculations usually follow the Hartree-Fock approximations. For details on the non-relativistic and relativistic approaches, see Section 4.2.6 of International Tables of Crystallography, Volume C.
The dispersion of X-rays was theoretically predicted by Waller (Waller, I., 1928, Über eine verallgemeinerte Streuungsformel. Z. Phys. 51, 213-231.) and first calculated by Hönl (Hönl, H., 1933, Zur Dispersionstheorie der Röntgenstrahlen. Z. Phys. 84, 1-16; Hönl, H., 1933, Atomfactor für Röntgenstrahlen als Problem der Dispersionstheorie (K-Schale). Ann. Phys. (Leipzig), 18, 625-657.
Section 4.2.6 of International Tables of Crystallography, Volume C