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 . 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 .
FEFF calculates the full complex-valued fine structure function
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 by ; j is the index of a particular scattering path; N is the total number of possible paths; is the many-body amplitude reduction factor; is the effective path length of path j (which is 1/2 of the total path length); is the effective curved wave scattering amplitude for path j; is the l=1 phase shift at the atom which emits the photoelectron; is the effective XAFS Debye-Waller factor for the path; and 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 and use the imaginary part
to obtain the XAFS ,