Relativistic tight-binding calculation of core-valence transitions in Pt and Au

The results of a relativistic tight-binding energy-band model for Pt and Au, utilizing parameters derived from Smith's empirically adjusted combined interpolation scheme, are applied to calculate the one-electron contribution to various x-ray and energy-loss spectra involving $4f$ and $2p$ core states in these materials. These results show that the unoccupied holes in the Pt $5d$ bands have predominantly $j=\frac{5}{2}$ character (${h}_{\frac{5}{2}}$) such that the ($\frac{{h}_{\frac{5}{2}}}{{h}_{\frac{3}{2}}}$) ratio ranges from \ensuremath{\sim}3.5 within 0.5 eV of ${E}_{F}$ to \ensuremath{\sim}2.9 over the entire unoccupied conduction band. Taking into account dipole transition probabilities, the former ratio leads to a predicted line-strength ratio $\frac{{I}_{{N}_{7}}}{{I}_{{N}_{6}}}\ensuremath{\approx}2.9$ near threshold for excitations involving the $4f$$j=\frac{7}{2}({N}_{7})$ and $j=\frac{5}{2}({N}_{6})$ core levels in Pt. This result is in good agreement with the corresponding experimental ratios that are derived from electron energy-loss (2.5) and x-ray-absorption (2.3) spectra. Comparable agreement is obtained between the calculated and observed (electron-energy-loss) $\frac{{I}_{{N}_{7}}}{{I}_{{N}_{6}}}$ ratios in Au. The present results are applied to calculate the ${N}_{6}\ensuremath{-}{N}_{7}$ x-ray emission spectra in both Pt and Au and to interpret the ${L}_{2}\ensuremath{-}{L}_{3}$ absorption-edge data in Pt.