Yb $3d$ x-ray photoelectron spectroscopy (XPS) and $L$-edge x-ray absorption spectroscopy (XAS) are powerful techniques for determining the valence state of Yb compounds. In particular, $L$-edge XAS directly probes optical transitions from the Yb $2p$ core level into unoccupied Yb $5d$ states, thereby providing access to the broad conduction band derived from Yb $5d$ orbitals. In this study, we demonstrate that properly accounting for the band-shape effect is essential for a reliable analysis of $L$-edge XAS spectra. For ${\mathrm{YbAl}}_3$, we compared high-energy-resolution fluorescence-detected XAS (HERFD-XAS) with theoretical spectra based on an impurity Anderson model and identified characteristic spectral features that reflect the Yb $5d$ band structure obtained from first-principles calculations. To resolve ambiguities in the interpretation of the $L$-edge XAS arising from the band-shape effect, we incorporated available XPS data, and both the HERFD-XAS and XPS spectra were consistently reproduced using a single electronic-state model. In addition to extracting the band-shape information, our analysis further suggests the presence of a finite interorbital Coulomb repulsion ($U_{\mathrm{fd}}$) between the Yb $4f$ and $5d$ states.

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• Density of states
• Electronic structure
• Kondo effect
• Anderson impurity model
• Hard x-ray photoelectron spectroscopy
• X-ray absorption spectroscopy