Quantum Statistical Approach to Debye-Waller Factor in EXAFS, EELS and ARXPS. II. Application to One-Dimensional Models

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Abstract
Temperature dependence of Debye-Waller factor in EXAFS, EELS and ARXPS is calculated for one-dimensional models on the basis of first principle quantum statistical method developed in the previous paper I. In contrast to diffraction Debye-Waller factors for crystal we have no need to worry about the divergence for these thermal factors in one- and two-dimensional phonon systems. We consider anharmonic Morse potential as nearest neighbor interaction. We take up to quartic term into account and estimate up to fourth order cumulants for both monatomic and diatomic chains in wide temperature range from low temperature in which quantum effect is important, to high temperature in which classical approximation works. Characteristic features of the contributions from optical and acoustic modes are discussed in the diatomic model chain. The result obtained here give us clear physical insights of those thermal factors.