Quantum theory of post-collision interaction in inner-shell photoionization: Final-state interaction between two continuum electrons

In inner-shell photoionization followed by Auger decay, the Auger electron initially screens the ionic Coulomb field ‘‘seen’’ by the photoelectron. This screening phenomenon affects the post-collision interaction that shifts the Auger energy and distorts the line shape. The analytical Auger electron line-shape formula which we derived previously on the basis of asymptotic Coulomb wave functions is now modified to account for the screening effect. The ionic charge seen by the photoelectron is reinterpreted on the basis of asymptotic properties of the continuum wave function pertaining to two outgoing electrons. It is shown that this procedure is consistent with semiclassical models which account for the time required for the Auger electron to overtake the photoelectron. Our modified Coulomb line shapes are found to agree perfectly with the semiclassical line shapes for photon excess energies $E_{\mathrm{exc}\mathrm{\gtrsim }({\Gamma }_i{\varepsilon }_A{)}^{1/2}}$, where ${\Gamma }_i$ is the width of the initial hole state and ${\varepsilon }_A$, the Auger electron energy. Agreement between the present theory and recent synchrotron-radiation measurements consequently becomes excellent in this range of photon energies as well.