Multiplet splitting of final-state configurations in x-ray-absorption spectrum of metal V${\mathrm{O}}_2$: Effect of core-hole-screening, electron correlation, and metal-insulator transition

X-ray-absorption $K$-edge spectra of the V $1s$ core level in V${\mathrm{O}}_2$ exhibit broadening and splitting of the $1s\to t_{2g}$ core transition at the $K$ threshold at the semiconductor-to-metal phase transition. The three components observed in the metallic phase are assigned to final-state configurations characterized by different occupation numbers of the localized $d_{\parallel }$ band at the Fermi level: $d_{\parallel }^2$, $d_{\parallel }^1$, and $d_{\parallel }^0$. In the low-temperature semiconducting phase only the $d_{\parallel }^1$ final-state configuration is present. This experiment shows the core-hole-induced relaxation in x-ray-absorption spectroscopy of a narrow-band metal, where electron correlation is not negligible.