Generalized Franck-Condon principle for resonant photoemission

A generalized Franck-Condon (GFC) principle for resonant x-ray Raman scattering and for resonant photoemission in particular is derived and numerically investigated. The GFC amplitudes differ from ordinary FC amplitudes by the presence of photon and photoelectron phase factors which describe the coupling—or interference—of the x-ray photons or Auger electrons with the nuclear motion. With the GFC amplitudes, a Kramers-Heisenberg relation is obtained for vibronic transitions that corrects the so-called lifetime-vibrational interference formula. For resonant photoemission in the soft-x-ray region involving typical bound potential surfaces, the generalization gives a contribution to the FC factors that can amount to 20%. For core excitation above the dissociation threshold, the GFC principle relates to Doppler effects on the ejected photoelectron both for the so-called “molecular” and “atomic” bands. The role of the GFC principle in direct photoionization is briefly discussed.