Many-body processes in x-ray photoemission line shapes from Li, Na, Mg, and Al metals

Abstract

X-ray photoemission from all the accessible core levels in Li, Na, Mg, and Al have been measured with Al $K\alpha$ radiation from metal films evaporated in ultrahigh vacuum, and the asymmetric line shapes of the core-level spectra were analyzed in terms of the Doniach-Šunjić (DS) function. Observed lifetimes were compared with theoretical calculations and showed generally good agreement for the $1s$ and $2p$ levels of Na, Mg, and Al but poor agreement for the $2s$ levels. The Li $1s$ lifetime was found to be considerably longer than predicted from simple atomic calculations, but was in good accord with a more recent many-body calculation. Singularity indices were determined from data extending to within half the Fermi energy from the main peak. The range of validity of the DS function and the possible line shape interferences from other sources were carefully examined, showing that the electron-hole pairs measured in the asymmetic tails are an intrinsic property of the bulk-metal spectrum and that the DS function gives an excellent representation of the data over a wide range of energies. The magnitude and trend of the singularity indices for Na, Mg, and Al were interpreted in terms of the partial screening charges associated with the hole-state atom and were found to compare favorably with several recent calculations. Detailed investigation of temperature-dependent phonon broadening magnitudes and zero-point and phonon cutoff energies were carried out for Li, indicating that a recently proposed interference effect may be responsible for the anomalously large line-shape broadening in that metal. At present, however, no theory adequately accounts for the observed Li $1s$ linewidth. For Na, Mg, and Al, on the other head, enhanced broadening effects were not observed and recent calculations of phonons broadening agreed well with our measurements. The Li $1s$ binding energy was observed to be temperature dependent, and its magnitude and trend were explained by a combination of anharmonic lattice expansion and the heretofore unappreciated temperature dependence of the electronic screening energy. The surface plasmon energy of clean Li was found to be in marked disagreement with that predicted from the empirical bulk plasmon energy and simple free-electron theory and still remains to be explained. The validity of the sudden approximation used in the interpretation of the electron-hole pair and phonon spectra observed in this work is also discussed.