Theory of electron-phonon interaction in XAFS and other spectroscopies

The electron-phonon interaction in X-ray absorption and photoemission spectra are studied on the basis of nonrelativistic Keldysh Green's function theory developed by the authors. The X-ray absorption intensity is described in terms of reducible polarization propagator which can be written by using the electron irreducible polarization and the screened Coulomb interaction with and without the electron-phonon interaction. The lowest-order term naturally describes the Debye-Waller and the Franck-Condon factors, and also finite mean free path due to the electron-phonon interaction. We also derive a general formula to discuss low energy photoemission taking the electron-phonon interaction.