According to the Franck-Condon principle, transition probabilities between two molecular states are determined by the electronic transition probability, weighted by the overlap of the two vibrational states involved. In this paper we discuss a situation where this approximation is invalid, namely the tunnelling ionisation of H_2. The fragmentation of H2 in intense laser fields of visible and infrared wavelengths has been studied experimentally for more than a decade. It is usually assumed that the complete fragmentation occurs in three, more or less independent, steps. First there is the ionisation of H_2. Due to the small photon energy, the high ionisation potential and the absence of appropriate resonances, the ionisation takes place in the tunnelling or even the over-the-barrier regime. This type of ionisation occurs at the peaks and troughs of the coherent electromagnetic wave, i.e. in short periods of less than 1 fs during which the vibrational motion is essentially frozen. Quite naturally this leads to the idea of vertical transitions centered on the equilibrium distance of H_2, see e.g. Walsh et al. (1998). The population distribution amongst the vibrational levels of H_2~+ is then given by the standard Franck-Condon factors, which are shown in figure 1. However, it would be more accurate to take the large deformation of the H_2~+ electronic ground state in the strong laser field into account. This would be expected to shift the population towards higher vibrational levels , but we have strong reasons to believe that the population distribution is actually shifted towards lower levels.
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