The energy position of the occupied and unoccupied $4f$ levels relative to the Fermi energy is studied for the rare-earth metals. This is done by treating the excited state as an impurity in an otherwise perfect crystal. This picture is first considered in the complete screening approximation. In this approximation thermochemical data can be used directly to give energy values for the unoccupied $f$ levels which are accurate to ±0.05 eV; for the occupied $f$ levels the uncertainty is somewhat larger. The obtained values are then compared with recent x-ray photoemission spectroscopy (XPS) and Bremsstrahlung isochromat spectroscopy (BIS) data. The deviations found are discussed in terms of impurity effects left out in the complete screening approximation. When these effects are included a general good agreement with experiment is obtained. The consistency found in the XPS results is utilized for an improved estimation of the fourth ionization energy of the rare earths.

• Received 17 January 1979

DOI:https://doi.org/10.1103/PhysRevB.20.1315