Relativistic Calculation of Anomalous Scattering Factors for X Rays

TLDR

Relativistic photoelectric cross‑section calculations were performed and the principal contribution to Δf′ was numerically integrated without approximating the cross‑section energy dependence. Relativistic calculations produced Δf′ and Δf″ values for Cr, Fe, Cu, Mo, and Ag Kα radiations across elements Li–Cf, revealing significant differences from earlier work and improved agreement with experimental data for Δf″ and most rare‑gas Δf′, suggesting higher accuracy.

Abstract

Anomalous scattering factors Δf′ and Δf″ have been calculated relativistically for Cr, Fe, Cu, Mo, and Ag Kα radiations for the atoms Li through Cf. An interpolation scheme for other wavelengths is included in a separate report. Relativistic calculations of the photoelectric cross section have been made and the integral for the principal contribution to Δf′ has been evaluated numerically without approximation to the form of the cross section-vs-energy curve, as has been done in previous calculations. Many of the results are significantly different from previous calculations. Where experimental values exist, agreement for Δf″ is improved. For the rare gases, except for xenon, agreement between Δf′ and experiment is improved. Because of the more rigorous evaluation of Δf′ from cross-section information, it is presumed that the present Δf′ values are more accurate than previous calculated values. Calculated mass absorption coefficients for the elements are included as incidental information.