Theory of the extended x-ray-absorption fine structure

A general theory of the fine structure observed on the high-energy side of the $K$-absorption edge (EXAFS) is presented. The form of the theory presented is useful when the excited atom is not too highly ionized and the potential is approximately spherically symmetric. A critical analysis is made of long-range-order theories of EXAFS and it is shown that the coherent effects of the periodic potential are not the dominant mechanism as assumed previously. The dominant mechanism is the scattering in the vicinity of the absorbing atom, and can most naturally be calculated by considering only the immediate environment surrounding the absorbing atom. Fourier-transforming EXAFS data determines the spatial dependence of a scattering matrix. This scattering matrix is expected to peak at the location of surrounding atoms, locating them, and can give information on the type of surrounding atoms and possibly the surrounding valence electron density. Because the $K$ edges of different atoms are separated, such information can be obtained around each atom type separately, making EXAFS a potentially powerful tool for determining the microscopic structure of condensed matter.