Recoil-induced vibrational excitation in inner-shell photoelectron spectra: Beyond the linear coupling model

The interplay between Franck-Condon and recoil-induced vibrational excitation in core-electron photoionization has been investigated using generalized Franck-Condon factors. Three models for the vibrational wave functions have been considered: the linear-coupling model, the harmonic oscillator, and the Morse oscillator. At every level it appears that the two processes can be treated as independent, and the total vibrational excitation energy is simply the sum of the excitation energies characteristic of the two processes. At the level of the linear coupling model, the vibrational excitation profile is exactly the convolution of the profiles for the two different processes; for the other levels of approximation the overall profile differs only slightly from the convolution. The results also show that the vibrational intensity ratio, Rv=(v=1)/(v=0), varies linearly with the vibrational excitation, but that the proportionality constant relating these two quantities is not ℏω2, as has been previously assumed, but ℏω1 (where ω1 and ω2 are the characteristic vibrational frequencies of the neutral and ionized molecules, respectively).