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Hard x-ray photoemission and optical spectroscopies have been performed onYbS and Yb metal to determine the precise $f$-electron occupation. A comparisonof the photoemission spectra with the energy loss functions in bulk andsurface, obtained from optical reflectivity, enables us to distinguish betweenthe energy loss satellite of Yb$^{2+}$ peak and Yb$^{3+}$ multiplet. Theresults clearly indicate a purely divalent Yb state except for the surface ofYbS. We demonstrate that the present method is highly reliable in identifyingthe electronic structure and the mean valence in $f$-electron systems.

Combining photoemission and optical spectroscopies for reliable valence determination in YbS and Yb metal