Lorentzian line shape due to an inhomogeneous size distribution without relaxation

In this paper, it is demonstrated that a Lorentzian line shape is predicted for a resonance interacting with a bath of equally spaced levels, even in the sparse, low density of states limit, if one performs an inhomogeneous average over the position of the bath states relative to the bright state. The implication for the spectroscopy of molecules in helium nanodroplets and possibly other samples with a significant size distribution is that coupling of excitations to phonons can lead to Lorentzian shaped transitions entirely from inhomogeneous broadening with no population relaxation in the sample.