Phonon effects on X-ray absorption and X-ray photoemission spectra

Some important phonon effects observed in X-ray absorption and X-ray photoemission spectra are discussed on the basis of nonequilibrium Green's function theory. This theoretical framework allows us to incorporate phonon effects, such as Debye-Waller (DW) factors, Franck-Condon (FC) factors and electron-phonon interactions in a natural way. In the case of core level excitations, we can take into account the core-hole effects in lesser Green's function g< and photoelectron propagation in greater Green's function g>. For the core-hole propagation we derive some formulas to describe the thermally displaced core functions: we have p components even for deep core s orbital due to the thermal motion. We should notice that the thermal fluctuation is quite small but it is already in the order of the spread of the core functions. Applying Mermin's theorem, we can calculate the thermal average of the hole propagator g<: here an important ingredient is the Debye-Waller factor used in X-ray and neutron diffraction. For the pre-edge structures, the intensity associated with forbidden electric dipole transition is sensitive to the temperature compared with allowed electric quadrupole transition. We also discuss the FC and their interference, which have negligible contribution to pre-edge intensity and energy shift. The quasi-particle energy is also influenced by the core displacement which can be responsible for the peak shift of the pre-edges. We also discuss the changes of the photoelectron angular distributions caused by the thermal atomic vibration.