Scattering factor calculations and dispersion corrections for heavy atoms

Abstract

Reliable knowledge of the complex X-ray form factor (Re( f) and Im( f)) is required for crystallography, deformation density bonding studies and refractive index studies. Dispersion corrections are important in DAFS, MAD analyses and XAFS studies. Discrepancies between currently used theoretical approaches of 200% exist for numerous elements from 1 to 3 keV X-ray energies, and at higher energies these discrepancies can persist at the 10% level or more. This has suggested that new formulations and new experimental approaches are necessary. Recent tabulations improve upon the theoretical uncertainty in some of these regions by a factor of 10 and reduce the error of this approach to below one standard deviation. Recent experimental developments have begun to probe alternate theory, providing a tool to investigate the significance of relativistic corrections and convergence criteria across a range of atomic number. In part, this has revealed that more theoretical work will be required in future years. Recent advances permit new probes and insights into atomic and solid state physics, as well as to many X-ray optical applications. This paper discusses significant improvements upon the theoretical uncertainty in near-edge regions, reducing the error of this approach to less than one standard deviation.