The nuclear dynamics accompanying the excitation to and the subsequent decay of an electronic state is discussed. Particular attention is paid to cases, in which the whole process cannot be divided into two steps (excitation and decay) since the excitation and the decay times are of the same order of magnitude. The recently introduced time-dependent formulation of the theory describing the wave packets' dynamics is extended to include the excitation process. The wave packets can be related to the intensity of the emitted particles. Most of the resulting integrals can actually be performed by employing eigenstates of the Hamiltonians corresponding to the involved potential energy surfaces. This leads to the so called ''timeindependent'' formulation of the theory. Computational details of the implementation of the corresponding ''timedependent'' and ''time-independent'' methods are presented. Illustrative applications are given to illuminate both the influence of the excitation process and the lifetime of the decaying state. It emerges that the intuitive interpretation of the spectra (within the above two step model) may fail. Insight into the process is gained by studying the evolution of the spectra as a function of time. The appearance of ''atomic lines'' due to dissociative decaying and final states is investigated in some detail.PACS: 33.80.!b; 32.80.Hd; 42.55.Vc
I IntroductionThe spectroscopic methods which involve the appearance of an excited decaying electronic state can roughly be divided into absorption or emission spectroscopies. In the first class the excitation process, i.e. the transition between the initial and the intermediate, decaying state is observed. Examples are conventional optical absorption spectroscopies and electron energy loss spectroscopy (EELS). In the emission spectroscopies the decay of the excited electronic state is studied. Under these spectroscopies come methods like X-ray emission spectroscopy (XES), Auger electron spectroscopy (AES) or the autoionization of coreexcited states.This classification is useful if the effects of nuclear dynamics on the detected spectra are considered. In absorption spectroscopies the nuclear dynamics leads in combination with the finite lifetime of the excited state only to a broadening of the observed bands. In emission spectroscopies, however, additional effects due to interference phenomena may occur. Apart from band broadening the bands can be energetically shifted and asymmetric band forms may be introduced [1, 2]. These effects are the strongest if the lifetime of the decaying state is in the range of the typical times of internal vibrations in this state.If the excitation time is of the same order-of-magnitude as both the lifetime of the decaying state and the typical time of internal vibrations, further effects in the spectra may appear. Then, the observed spectra are also influenced by the duration and other details of the excitation. In these cases the excitation process cannot be regarded as an instantaneous process, which can be separated...