Theory of extended x-ray absorption fine structure: Single and multiple scattering formalisms

A generalized formalism for the EXAFS effect is presented. The full T operator in the Lippmann–Schwinger equation is expanded and the first term and part of the second term are seen to effectively correspond to single scattering EXAFS processes. The latter term includes secondary scattering by the absorber, and within this formalism it is this term that introduces the central atom phase shift. The expression obtained for the single scattering problem is identical with that found by other investigators. A solution to the general EXAFS problem involving an absorbing atom and two neighboring atoms is also presented. The expression differs from that previously reported [B. K. Teo, J. Am. Chem. Soc. 103, 3990 (1981)]. Multiple scattering is seen to contribute increasingly to the EXAFS as the three atoms approach colinearity. Both the amplitude and frequency of the multiple scattering components are functions of the geometry of the system. The model systems studied indicate that, in many cases, multiple scattering effects must be considered in the analysis of non-nearest-neighbor shells. The theory may readily be extended to systems and scattering paths of arbitrary complexity.