Time-dependent theory of the Auger resonant Raman effect for diatomic molecules: Concepts and model calculations for N₂ and CO

We develop an explicitly time-dependent theory for one-step resonant excitation-deexcitation processes of core electron states in diatomic molecules. Emphasis is placed on a conceptual picture demonstrating how the effective time of the formation of the spectra—which is influenced by the bandwidth of the exciting radiation, by the excitation of the molecule being resonant or off resonant (detuned), and by the actual core hole lifetime—changes the appearance of the deexcitation electron spectra. Explicit time-dependent model calculations for three final states each of 1s-hole excited N₂ (including one spectator decay) and C1s–hole excited CO allow demonstration of the various consequences for the spectral shapes which derive from these influences. In particular, off-resonance excitation is shown to shorten the effective time of the spectrum formation below the lifetime of the core-excited state leading to the recently observed collapse of the vibrational structure in the spectrum. Our calculated spectra also demonstrate the influences of the relative positions and shapes of the potential curves involved. On resonance, the nodal structure of the vibrational wave functions of the core-excited state is reflected in the shapes of the spectator decay spectra of N₂ with a soft final state interatomic potential.