Choice of dipole operator gauge in time-dependent R-matrix theory

We investigate multi-photon ionization of helium using the time-dependent R-matrix method in order to assess the best choice of gauge for the description of the laser field when the system under investigation is a multi-electron system. Ionization probabilities are obtained using the length gauge and the velocity gauge and various He basis sets, when a minimum of three or four photons need to be absorbed to achieve ionization. The probabilities are found to converge for both gauges as the number of orbitals used in the basis set increases, but they are more consistent in the length gauge. Ionization probabilities can be compared to those derived from other theoretical calculations. Agreement is within 10% when ionization requires absorption of at least three photons, but the differences increase to 20-50% when absorption of four photons is required. Analysis of the multi-photon matrix elements provides further evidence for better consistency in the length gauge than the velocity gauge when high-lying states are excluded from the calculations, which is, at present, unavoidable for a multi-electron system.