3d x-ray-absorption lines and the 3$d^9$4$f^{n+1\mathrm{}}$ multiplets of the lanthanides

We have measured and calculated the 3d ($M_4$,5) absorption spectra for all the rare-earth metals, as well as the full 3$d^9$4$f^{n+1\mathrm{}}$ multiplets for the early and late rare earths. The quality of agreement between theory and experiment is excellent, except for Sm. In x-ray-absorption spectroscopy (XAS), only dipole selected lines are seen but all multiplet effects can be observed in x-ray photoemission spectroscopy. The line shapes and 3d-4f interactions are discussed. Our results provide an improved basis for use of the 3d XAS spectra for studies of ‘‘mixed-valence’’ systems.