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Calculation of the EDAFS contributions using FEFF

As discussed in the introduction, DAFS is intimately connected to XAFS by unitarity and causality. Here, we describe the calculation of the diffraction fine structure using the causal, unitary generalization of the MS-XAFS formalism. The original EXAFS theories were single-scattering plane-wave theories [20]. The curved-wave and multiple-scattering effects can be quite important, however, and recently an accurate and computationally efficient code, called FEFF, which includes these effects, has been developed [4].

FEFF calculates the full complex-valued fine structure function tex2html_wrap_inline1458 by summing over all possible photoelectron scattering paths,
where the photoelectron wavenumber, K, is related to the incident photon energy E and the binding energy tex2html_wrap_inline1346 by tex2html_wrap_inline1342; j is the index of a particular scattering path; N is the total number of possible paths; tex2html_wrap_inline1472 is the many-body amplitude reduction factor; tex2html_wrap_inline1348 is the effective path length of path j (which is 1/2 of the total path length); tex2html_wrap_inline1478 is the effective curved wave scattering amplitude for path j; tex2html_wrap_inline1482 is the l=1 phase shift at the atom which emits the photoelectron; tex2html_wrap_inline1486 is the effective XAFS Debye-Waller factor for the path; and tex2html_wrap_inline1488 is the combined mean free path and core hole lifetime factor.

All state-of-the-art theoretical EXAFS codes actually calculate the full complex-valued x-ray diffraction tex2html_wrap_inline1490 and use the imaginary part to obtain the XAFS tex2html_wrap_inline1454,