Hole Recoil, Vibrational Shake-up, and Photoelectron Lineshapes

The general problem of boson renormalization of a quasi-localised hole state created in a photo-ejection process from a molecule or solid is considered. A quasi-localised hole can hop from the initial site of creation and this introduces the possibility of recoil when the hole interacts with the boson field. As an illustrative example, the problem of the photoionization spectrum for a molecule adsorbed on a metal surface is considered. Hopping from the admolecule hole state into the substrate is the delocalization mechanism and intra-molecular vibrational modes are the bosons. Recoil induced interferences between the two processes lead to a more narrow lineshape than would be inferred from a straightforward convolution-of-independent-events line.