X-Ray Photoemission from Zinc: Evidence for Extra-Atomic Relaxation via Semilocalized Excitons

X-ray-photoelectron-spectroscopy studies on clean metallic zinc are reported. A well-defined Fermi edge was observed, and the $3d$ band peak was located at ${E}_{F}\ensuremath{-}10.2$ eV. The data analysis raised the question of the extent to which valence-band photoemission spectra of metals are distorted, relative to one-electron "frozen-orbital" band-structure calculations, by differential relaxation. Atomic hole-state calculations by Lindgren and by Gelius and Siegbahn indicate that (intra-) atomic relaxation can vary by up to 5 eV between $3d$ and $4s$ shells. Thus valence-band spectra in $3d$ transition metals can be seriously distorted by atomic relaxation alone. It is argued that the $3d$ bands probably lie below the $4s$, $4p$ valence bands in zinc in the initial state, but not in the photoemission spectrum. The nickel photoemission spectrum may well be distorted by relaxation. The magnitude of the extra-atomic relaxation energy $\ensuremath{\Delta}{E}_{B}$ was estimated in several ways. Empirical estimates were based on comparisons among photoemission and optical data on several elements. Semiempirical estimates were based on theoretical atomic binding energies and experimental binding energies in metals. All estimates were in rather good agreement, showing extra-atomic relaxation energies of up to \ensuremath{\sim} 15 eV. A theoretical model was derived, based on the assumption that extra-atomic relaxation occurs through screening of the hole state by formation of a semilocalized exction. This process was described by Friedel as positive phase shifts in the conduction bands. The model predicts a slow rise in $\ensuremath{\Delta}{E}_{B}$ in the $3d$ series and a sudden drop between Ni and Cu, in excellent agreement with experiment.