Theory of extended x-ray absorption fine structure: One-dimensional model calculations

We present formulas for the calculation of extended x-ray absorption fine structure in one-dimensional models. The formulas are entirely analogous to the three-dimensional expressions in terms of Green's functions, but have the heuristic advantage that they may be exactly evaluated. For a Kronig-Penney model we evaluate these equations and compare with several approximation schemes, based on either "short-range order" or "long-range order" points of view. With the use of a reasonable broadening to represent inelastic processes, these approximations all agree quite well with the exact calculation.