Probing the time-dependent decay of molecular core-excited states: The Auger resonant Raman effect forO2

We use our recently developed explicitly time-dependent theory for one-step resonant excitation-deexcitation processes of core-excited states in diatomic molecules to investigate the $\mathrm{O} 1s$ core-hole decay electron spectra of ${\mathrm{O}}_{2}.$ Looking at the changes of the spectra as the exciting radiation frequency is tuned to and away from the excitation resonance allows us to follow the time evolution of the nuclear degrees of freedom of the molecule in the short-living core-excited state. We explicitly demonstrate that here, in contrast to other diatomic molecules such as ${\mathrm{N}}_{2}$ or CO investigated earlier, the relative softness of the intramolecular bond in the core-excited state allows us to interpret changes in some gross features of the decay spectra with varying photon energy in terms of the classical time evolution in the excited state. In particular, the low-energy tail of the electron spectra, due to the fraction of the core-excited state molecules surviving longest, gets visibly suppressed if the exciting radiation is detuned away from the x-ray-absorption resonance.