Multiple-scattering regime and higher-order correlations in x-ray-absorption spectra of liquid solutions

By making a comparison between the Mn K-edge absorption of (MnO₄) ^- and Mn (H₂O) ₆^2+ complexes in aqueous solution we obtain an experimental determination of the energy extent of the type-II multiple-scattering (MS) regime that is substantially wider than expected. Theoretical calculations based on the MS formalism support this conclusion. We also recognize three energy regions in the absorption spectra of these complexes: a full MS region, where numerous or an infinite number of MS paths of high order contribute (depending on whether the MS series converges or not), an intermediate MS region, where only a few MS paths of low order are relevant, and a single-scattering region where the photoelectron is backscattered only once by the ligands extended x-ray-absorption fine-structure (EXAFS) regime. Theoretical considerations show that this must be a general situation in x-ray-absorption spectra and opens the way to a unified scheme for their interpretation. The energy extent of the three regions is obviously system dependent. We also show how to generalize to MS contributions the usual EXAFS analysis using curved-wave propagators and indicate how to extract geometrical information from the spectra of the two clusters investigated. In particular the method is used to derive the Mn---O---O---Mn path length in the (MnO₄) ^- complex.