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 ∼3.5 within 0.5 eV of $E_F$ to ∼2.9 over the entire unoccupied conduction band. Taking into account dipole transition probabilities, the former ratio leads to a predicted line-strength ratio $\frac{I_{N_7}}{I_{N_6}}\approx 2.9$ near threshold for excitations involving the $4f$ $j=\frac{7}{2}\left(N_7\right)$ and $j=\frac{5}{2}\left(N_6\right)$ 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 $N_6-N_7$ x-ray emission spectra in both Pt and Au and to interpret the $L_2-L_3$ absorption-edge data in Pt.