Solid State Communications, Vol. 58, No. 9, pp. 595-599, 1986. Printed in Great Britain. 0038-1098/86 $3.00 + .00 Pergamon Journals Ltd. THREE PARTICLE CORRELATION FUNCTION OF METAL IONS IN TETRAHEDRAL COORDINATION DETERMINED BY XANES J. Garcia*, M. Benfatto and C.R. Natoli INFN Laboratori Nazionali di Frascati, 00044 Frascati, Italy A. Bianconi Dipartimento di Fisica, Universita "La Sapienza", 00185 Roma, Italy and I. Davoli and A. Marcelli Dipartimento di Matematica e Fisica, Universita di Camerino, 62032 Camerino, Italy (Received 4 January 1986 by F. Bassani) The three particle correlation function of local atomic distribution at metal ion sites in solutions has been extracted from XANES (X-ray absorp- tion near edge structure) spectra of [CrO4 ] 2- and [MnO4 ] - ions measured by using synchrotron radiation. The absorption cross section for ls core level excitation is calculated in the real space multiple scattering approach using the Hedin and Lundqvist energy dependent potential. We show that in these systems the expansion of the total absorption cross section in terms of contributions of higher order scattering processes is possible over a large energy range. This gives a unified theory of XANES and EXAFS and allows the third order correlation function to be extracted from experimental data. ACCORDING TO THE FERMI golden rule for optical transitions the absorption coefficient for excitations from a core level to an unoccupied state at energy E can be calculated in k-space and the measured adsorption coefficient is given by a(E)= P(E).D(E), where P(E)is the transition matrix element and D(E) the projected particle density of states. As pointed out by Papacon- stantopoulos et al. [1 ] the finite lifetime of the excited photolectron in a high energy conduction band in the range of tens of eV above the Fermi level is an essential physical aspect of core transitions that cannot be neg- lected. It has been demonstrated [2, 3] that the absorption cross section for core transition can be solved in real space using the Green function approach in the frame of multiple scattering theory. In this approach the limited mean free path of the photoelectron enters directly in the theory determining the finite size of the cluster of neighbouring atoms around the absorbing atom. The important aspect of the solution of the absorp- tion cross section in the real space is that physical pro- cesses determining the unoccupied density of states in * Permanent address: Department of Thermology, Zaragoza University, Spain. condensed matter appear explicitly. The wavefunction of the excited photoelectron turns out to be determined by the scattering from neighbouring atoms and therefore the spectra probe the geometrical atomic distribution and interatomic distances. Two parts of the spectra have been identified experimentally: the XANES [4] (X-ray absorption near edge structure) and the EXAFS (ex- tended X-ray absorption structure) [5]. At high energies such that the atomic scattering power becomes small (much less than one) a single scattering (SS) regime takes place, where the modulation in the absorption coef- ficient (EXAFS) is substantially due to the interference effect of the outgoing photoelectron wave from the absorbing atom and the backscattered wave from each surrounding atom. [6]. Hence this latter part of the spectrum provides information about the pair corre- lation function. By decreasing the photoelectron kinetic energy a gradual turn over occurs from the EXAFS (SS) regime to the XANES full multiple scattering (FMS) regime where all the MS pathways which begin and end at the absorbing atom contribute to the total absorption cross section. Here we present the results of a study of manganese and chromium K-edge spectra of ions in solution. We show that the absorption coefficient can be expanded in terms of successive multiple scattering events, classified 595