Systematic investigation of relativistic effects in EXAFS data analysis

Modern XAFS (x-ray absorption fine structure) data analysis is based on accurate multiple-scattering (MS) calculations of the x-ray absorption cross section, usually carried out solving the nonrelativistic Schr\"odinger equation for complex effective optical muffin-tin potentials describing the scattering of the atoms. The introduction of relativistic effects in extended XAFS (EXAFS) multiple-scattering calculations has been described in several papers and shown to be important for heavy atoms. However, few examples of applications and detailed studies of relativistic effects were given so far. In this work, we have performed a systematic investigation of relativistic corrections in systems of increasing atomic number, using a reliable simulation scheme recently developed and based on the incorporation of a pseudo-Schr\"odinger equation effectively replacing the Dirac relativistic form. Calculations have been put to a test in 12 different pure-element condensed-state systems, with the atomic number ranging from $Z=10$ for crystalline Ne to $Z=90$ for crystalline Th. The importance of accounting for relativistic effects has been highlighted for elements with $Z\ensuremath{\gtrsim}60$, as ones for which relativistic corrections for amplitudes of calculated XAFS MS signals exceed $10%$. The size of relativistic effects for calculated higher-order XAFS signal (with respect to the dominant single-scattering first-neighbor signal) has been shown, taking as example the ${L}_{3}$-edge spectra of crystalline Au and Pb. The size of relativistic effects for the $K$ and ${L}_{3}$ edges has been also evaluated, showing a slight increase of relativistic corrections for the ${L}_{3}$ edge. The improvement in the accuracy of XAFS simulations has been demonstrated comparing the results obtained for structural refinements of the ${L}_{3}$ edge of crystalline Au at 300 K.