Phonon broadening of x-ray photoemission line shapes in solids and its independence of hole state lifetimes

Using a simple model we show that the phonon contribution to photoemission line shapes is identical when the hole-state lifetime is either long or short compared to a typical phonon period. The principles are extended to Auger electron, x-ray absorption, and x-ray emission spectroscopies and should also be applicable to other excitation processes in x-ray photoemission. Experimental examples demonstrating these principles are cited.