X-ray-absorption spectroscopy andn-body distribution functions in condensed matter. I. Theory

The general theoretical framework underlying the GNXAS multiple-scattering (MS) data-analysis method for x-ray absorption spectroscopy (XAS) is presented. The main approximations leading to the reduction of the many-body process in that of a photoelectron scattering in an effective potential are summarized. The methods available to expand the extended x-ray-absorption fine-structure χ(k) into physically meaningful terms are described. In particular, emphasis is given to the definition of the irreducible n-body signals ${\gamma }^{\left(\mathit{n}\right)}$ that can be calculated directly by means of linear combinations of continued fractions, or by using their respective multiple-scattering series. It is found that even for an infinite system the expansion of the χ(k) signal in terms of ${\gamma }^{\left(\mathit{n}\right)}$ has a better convergence rate than the MS series. Simple expressions for performing the configurational averages of the structural signals in the presence of thermal and structural disorder are derived. These can be used for the structural analysis of molecular, crystalline, or moderately disordered systems. It is shown that in the case of highly disordered systems the expansion in terms of the ${\gamma }^{\left(\mathit{n}\right)}$ signals is the natural framework for the interpretation of the XAS signal. General equations for the ensemble-averaged χ(k) signal as a function of a series of integrals over the n-body n≳2 distribution functions ${\mathit{g}}_{\mathit{n}}$ are provided and the possible use of advanced strategies for the inversion of the structural information is suggested.