The influence of finite lifetime of electronic states on the vibrational structure of molecular electronic spectra

A general theory describing the effect of finite lifetime of electronic states on the vibrational structure of electronic spectra is developed. A proper description of the decay of the excited state involved in the transition is achieved by summing the perturbation series for the T matrix to infinite order in the interaction responsible for the decay. An effective non-hermitian hamiltonian is obtained which describes the vibrational motion in the short-lived electronic state. The finite lifetime influences the spectra in a different way, depending whether the shoft-lived state is the final or the initial state of the electronic transition. In the former case the spectrum is given by an incoherent superposition to lorentzian lines, while in the latter case there are interferences between the vibrational levels of the short-lived electronic state which modify the vibrational structure is a characteristic manner. The theory is applied to various spectra of CO and N₂ involving the excitation of K-shell electrons. Interferences effects are predicted and identified in the experimental spectra.