Quantum statistical approach to Debye-Waller factors in EXAFS, EELS and ARXPS IV. Anharmonic contribution in spherical-wave expression

In this work we have developed a new approach based on Brouder's Lie group formulas to include both spherical wave correction and anharmonic vibration effects, which is not limited to isotropic systems. We apply partial summation technique to get a plane wave part which does not disappear even for large kR limit, and a spherical wave part which disappears for that limit. The former part has just the same cumulants as those used for plane wave EXAFS formulas, however, the latter cannot be reduced to the ordinary cumulants and is closely related to the correction factor due to thermal vibration derived by Rennert within the harmonic approximation. The plane wave part already includes spherical wave effects of photoelectron scattering. Numerical calculations for K-edge EXAFS show that spherical wave thermal factors give rise to different phase from plane wave part, which can give peak shift in Fourier transformed EXAFS spectra. The polarization dependence is also discussed. (author)