Spin-density calculations for core-electron photoemission and Auger electron line shapes, x-ray-edge exponents, and solid-state shifts

Abstract

Spin-polarized density-functional conduction-electron screening calculations for core ionization and Auger transition for elements Li, Be, Na, Mg, Al, and Ca are performed. The screening is described by conduction-electron scattering phase shifts obtained from self-consistent-field ab initio calculations. Both spins are treated separately in order to study the spin-polarization effects. The core-electron states are resolved by a Hartree-Fock-Slater method, which makes it possible to apply the same local-density exchange and correlation approximation to all electrons, including the conduction electrons. X-ray-edge exponents and x-ray photoelectron (XPS) line singularity indices are extracted from the phase shifts. Auger line singularity indices are also evaluated. In the case of Na, Mg, and Al metals the results agree with those of the previous spin-symmetric calculations and experimental values. The screening of Li and Be is, however, strongly spin-polarized, which both increases the singularity index and decreases the edge exponents. This partly explains the broad $K$ edge of Li. The spin-polarized method seems to be necessary to describe the peculiar conduction-electron response to the core hole in Ca. The screening in this case is localized in energy, totally spin polarized, and of $d$-electron type. This should cause very broad x-ray edges and the most asymmetric XPS and Auger lines. By performing the corresponding free-atom calculations with the same method, the solid-state shifts (extra-atomic relaxation energies) for the photoelectron energies (binding energies) and Auger electron energies are obtained. The density-functional results agree better with the experiments than the results of the excitonic model or excited-atom model, for example. In the case of Ca the shift values are exceptionally large due to the localized $d$-electron screening.