Final-state rule for Auger line shapes

A final-state (FS) rule is proposed and tested for the Auger process. This rule is similar to the FS rule and the orthogonalized-final-state (OFS) rule already in existence for x-ray emission and absorption. The FS rule can be stated as follows: In the absence of significant configuration mixing, the initial state determines separately the $\mathrm{ss}$, $\mathrm{sp}$, and $\mathrm{pp}$ Auger intensities; the shape of each contribution is determined by the final density of states (DOS). Several Auger line shapes are examined in the context of this FS rule. In the molecules N$\mathrm{O}_3^{}{}_{}{}^{-}$, ${\mathrm{O}}_2$, and ${\mathrm{C}}_2$ ${\mathrm{H}}_6$, core-hole-state calculations indicate screening significantly alters the ground-state molecular orbital $p$ populations. The experimental Auger peak intensities, however, reflect $p$ populations similar to the ground state. In the metals Be and Cu, the $s$ electrons dominate the core-hole screening charge. This significantly increases the $\mathrm{ss}$ and $\mathrm{sp}$ contributions relative to the $\mathrm{pp}$, which is indicated by the experimental Auger line shape. The individual $\mathrm{ss}$, $\mathrm{sp}$, and $\mathrm{pp}$ line shapes, however, reflect the final DOS. The Auger line shapes of the ${\mathrm{C}}_8$Cs and ${\mathrm{C}}_6$Li intercalated graphite systems reflect a valence band appropriate to the final state; however, they exhibit a much larger intercalant peak intensity compared to photoemission data. This is discussed in light of the OFS rule.