Quantum Statistical Approach to Debye-Waller Factors in EXAFS, EELS and ARXPS. I. Anharmonic Contribution in Plane-Wave Approximation

Temperature dependence of EXAFS, EELFS and ARXPS is discussed in the framework of plane wave approximation, where we take the cubic and quartic anharmonicity into account. First we apply cumulant expansion whose expanded terms are written in terms of corresponding lower order moments and cumulants. Secondly we apply temperature Green's function technique systematically to calculate these moments for perfect crystals with translational symmetry. We furthermore discuss high and low temperature behavior of these cumulants, and also describe real space representation of them in comparison with widely used classical expression. This real space representation needs no translation symmetry, and we discuss the applicability of the classical local space integral formula.