Inclusion of local structure effects in theoretical x-ray resonant scattering amplitudes using ab initio x-ray-absorption spectra calculations

Improved calculations of Bragg peak intensities near atomic resonance are obtained by including the effect of the local environment around the resonant atoms on the resonant scattering amplitudes $\ensuremath{\Delta}{f=f}^{\ensuremath{'}}{+if}^{\ensuremath{''}}.$ Theoretical absorption cross sections calculated by the ab initio x-ray-absorption code FEFF are used to obtain the imaginary part ${f}^{\ensuremath{''}}$ by extension of the optical theorem to nonforward scattering under the dipole approximation. The real part ${f}^{\ensuremath{'}}$ is obtained by a limited range Kramers-Kronig transform of the difference between ${f}^{\ensuremath{''}}$ based on FEFF and existing theoretical calculations of ${f}^{\ensuremath{''}}$ based on an isolated-atom model. The atomic part of $\ensuremath{\Delta}f$ calculated by FEFF for the resonant atom embedded in the local potential is assumed to have spherical symmetry; however, no restriction is placed on the spectral features due to multiple scattering of the intermediate-state virtual photoelectron. Bragg peak intensities calculated in the kinematic approximation using the FEFF-based $\ensuremath{\Delta}f$ are compared to intensities calculated using the isolated-atom $\ensuremath{\Delta}f$ and to experimental data for Cu metal and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.8}$ at the Cu K absorption edge, and for ${\mathrm{UO}}_{2}$ at the U ${M}_{\mathrm{IV}}$ absorption edge.