Gauge aspects of scattering theory in the presence of lasers

The problem of the choice of the electromagnetic gauge is investigated in the framework of collision theory in the presence of strong radiation fields. Charged-particle potential scattering is considered as an example. The analysis is based on the dipole approximation for the radiation field, and on the velocity and length gauges. Distinguishing features of field-assisted particle scattering are, among others, that: (i) the assisting field is embodied in the theoretical treatment exactly, through field-embedded scattering states, and (ii) conventional (field-independent) perturbations are chosen as being responsible for the scattering event. As expected on general physical grounds, the same results are obtained in the two gauges at any order of the scattering potential in so far as the particle-field interaction is treated exactly. In the so-called low-frequency approximation, on the other hand, where the particle-field interaction is treated in a simplified way in the intermediate states, the length gauge is found to perform better than the velocity gauge. In particular, within a prescribed degree of accuracy, the results in the length gauge are arrived at in a more rapid way. A very peculiar role in this is played by the Goppert-Mayer unitary transformation connecting the two gauges.