Geometrical information in soft-x-ray appearance potential spectroscopy and Auger-electron appearance potential spectroscopy

A general formalism is presented for the calculation of geometrically induced structure in soft-x-ray appearance potential spectroscopy and Auger-electron appearance potential spectroscopy spectra. Electronic wave functions similar to those used in low-energy-electron diffraction theory are used to describe the incident electron and the excited-final-state electrons. The problem of calculating the excitation matrix element is discussed, and its relevant symmetry properties displayed. Model calculations assuming a constant "bare" excitation matrix element, a spherically symmetric electronic density of states, and $S$-wave scattering from the ion cores are performed for a cluster of nuckel atoms and for a cluster that models oxygen on a Ni(001) surface. These calculations exhibit the general features predicted by the formalism. In the context of this study, it appears that multiple-scattering effects will be important in any analysis of experimental data that requires a direct comparison with theoretical calculations.