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 where 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 the thermal factor plays an important role both in EXAFS and XPD analyses for the asymmetric potential with strong anharmonicity. At low temperature the cumulant expansion up to the second order for the thermal damping function agrees well with the self-consistent result, but up to higher orders should be taken into account for the phase function. At high temperature the result from self-consistent calculations shows the characteristic behaviour: the thermal damping function is negative in the high-k region for both strongly and weakly anharmonic systems. The cumulant approximation cannot reproduce this behaviour. For the strongly anharmonic systems the quantum result shows qualitatively different behaviour from the classical approximation at 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.