Path-integral approach to Debye-Waller factors in EXAFS, EELS and XPD for cubic and quartic anharmonic potentials

In this paper thermal effects in extended X-ray absorption fine structure ( EXAFS) and X-ray photoelectron diffraction (XPD) due to atomic vibration in cubic and quartic potentials are studied by use of Feynman's path-integral approach. This approach can be applied to strongly anharmonic systems wher e the cumulant analyses break down. It is closely related to the well known classical approach which is only valid at high temperature. The phase of t he thermal factor plays an important role both in EXAFS and XPD analyses fo r the asymmetric potential with strong anharmonicity. At low temperature th e cumulant expansion up to the second order for the thermal damping functio n agrees well with the self-consistent result, but up to higher orders shou ld be taken into account for the phase function. At high temperature the re sult from self-consistent calculations shows the characteristic behaviour: the thermal damping function is negative in the high-k region for both stro ngly and weakly anharmonic systems. The cumulant approximation cannot repro duce this behaviour. For the strongly anharmonic systems the quantum result shows qualitatively different behaviour from the classical approximation a t low temperature: the former does not show the negative values even in the high-k region, while the latter shows the phase inversion in the amplitude .