The anomalous scattering of X-ray photons at the K absorption edge of free atoms and molecules, calculated by means of the modified Kramers-Heisenberg dispersion formula

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Abstract
The energy dependence of the anomalous atomic scattering factor in the vicinity of the critical energy for excitation of the 1s electrons is calculated. The effect of the finite lifetime of the intermediate states, as well as the influence of strong exciton states, is included. The evaluation of the dipole matrix elements in the generalised and modified Kramers-Heisenberg formula is based upon hydrogen-like wavefunctions. Numerical results are given for the atoms Ne, Ar, Kr and the molecule HCl.