Anatomy of strong field ionization II: to dress or not to dress?

We analyse S-matrix-type approaches to strong-field ionization by an intense few-cycle laser pulse. We derive simple modi. cations of approximate S-matrix-type approaches that either neglect the effect of the ionic potential after ionization, or treat this potential perturbatively. We show how these modi. cations eliminate some crucial problems and artefacts, such as the 'curse of the displaced atom', associated with the choice of gauge in the strong field approximation. We then discuss how these approximate S-matrix-type approaches should be applied to dissociating molecules using the example of H-2(+). We show that suppression of electron tunnelling between the two fragments of the molecular ion introduces dramatic changes in the spectrum of high harmonic emission generated by an intense laser pulse that probes the molecular dissociation. For large internuclear distances and even when the active electron is fully delocalized between the two fragments, the high harmonic spectrum loses all traces of the conventional interference pattern associated with a two-centre molecular structure.