Theory of atomic displacement effects induced by core-hole production on EXAFS

The effect of atomic displacement on EXAFS after the core hole production is studied within the harmonic approximation for atomic vibration and single scattering approximation for the photoelectron wave. With aid of the Schwinger method, we obtain the Debye-Waller factor, the Condon factor and their interference term. The second term gives the damping of EXAFS and energy shift of the inner potential, and the last term gives rise to a phase factor as a linear function of photoelectron momentum k. The Condon factor and the interference term cancel each other as far as the side band effects are included, though each contribution is not negligible. Therefore the validity of the widely used Debye-Waller factor within the harmonic approximation is confirmed at least in EXAFS region. Numerical calculation estimates the order of those factors, and shows that the energy shift is negligibly small.