QUANTUM-STATISTICAL APPROACH TO DEBYE-WALLER FACTORS IN EXAFS, EELS AND ARXPS - VI - PATH-INTEGRAL APPROACH TO MORSE POTENTIAL SYSTEMS

In this paper thermal effects in X-ray Photoelectron Diffraction (XPD) and EXAFS due to atomic vibration in Morse potential are studied by u se of the Feynman's path integral approach. This approach can he appli ed to strongly anharmonic systems where the cumulant analyses break. I t. is closely related to the well-known classical approach which is on ly valid at high temperature. The phase of the thermal factor plays an important role both in XPD and EXAFS analyses for the asymmetric Mors e potential. At high temperature each cumulant integral diverges where as the classical approximation is satisfactory both for the phase and the thermal damping. On the other hand; at low temperature cumulants e xpansion converges because of the quantum fluctuation; For the descrip tion of the phase up to the third, and for that of the thermal damping up to the fourth cumulant should be taken into account. In this case the classical approximation is quite poor for the description of the t wo factors. For the quantum calculation with the weak quantum effect t he tunneling does not contribute to the peak shift in the probability density P(q) but to the broadening.