Band approach to the excitation-energy dependence of x-ray fluorescence ofTiO2

Excitation-energy dependence of $\mathrm{Ti} {L}_{2,3}$ soft x-ray emission spectra (XES) of a ${\mathrm{TiO}}_{2}$ single crystal is measured near $\mathrm{Ti} 2p$ threshold using tuneable synchrotron radiation at excitation energies ${E}_{\mathrm{exc}}=458.2--476.9\mathrm{eV}.$ It is found that the emission spectra exhibit normal soft x-ray emission features, which do not change with excitation energy and inelastic and resonant x-ray emission features (RXES), which strongly depend on the excitation energy. We are using a band approach in order to discuss the excitation-energy dependence of $\mathrm{Ti} {L}_{2,3}\mathrm{RXES}$ of ${\mathrm{TiO}}_{2}.$ The RXES process is described as a convolution of occupied and unoccupied d states in the intermediate and final states. In this procedure the d states are limited to those which lie in the energy interval ${E}_{\mathrm{exc}}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}E$ taking into account the rule of k conservation. We calculate the curves of restricted joint density of states using the full potential linearized muffin-tin orbital method and the results are found to be in reasonable agreement with the experimental $\mathrm{Ti} {L}_{2,3},$ RXES of ${\mathrm{TiO}}_{2}$ measured at different excitation energies.