Effect of the central atom potential on the extended fine structure above appearance potential thresholds

The formalism previously given for describing the extended fine structure above appearance-potential-spectroscopy (APS) thresholds is extended by incorporating the effects of the excited "central" atom potential in an exact manner. The excitation-matrix elements are expressed in terms of the exact wave functions of the central atom potential. This introduces a "phase renormalization" into the excitation-matrix elements and eliminates a previously noted "phase difference" between single- and multiple-scattering calculations employing a plane-wave basis set. A series of approximations is then made which leads to an expression for the APS extended fine structure in terms of sinusoidal functions and hence provides a rationale for a Fourier-transform analysis. Simple model calculations assuming a constant "bare" excitation-matrix element, a spherically symmetric electronic density of states, and only $S$-wave scattering from the atomic cores are performed for a cluster of atoms having the atomic geometry of bulk vanadium. These calculations display the major predictions of the formalism and indicate that for a given system there may be some optimal energy range for data analysis. The problem of electron characteristic losses is considered, and it is pointed out that in the small-momentum-transfer limit the simple dipole selection rules appropriate to a photon-excitation process again apply. This may obviate many of the problems introduced by multiple angular momentum final states in the APS process.