Choice of dipole operator gauge in time-dependentR-matrix theory

Abstract

Abstract.We investigate multi-photon ionization of Helium using the Time Dependent RMatrix 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 multielectron system.

Atomic harmonic generation in time-dependentR-matrix theory

“…Details of the method can be found in [12,23], so we only give a short overview here. The time-dependent Schrödinger equation for an atom containing (N + 1) electrons is…”

“…The laser field is described using the dipole approximation in the length form, and is assumed to be linearly polarized and spatially homogeneous. This form provides the most reliable ionization yields when only a limited amount of atomic structure is included [23].…”

“…The residual He + ion is represented through a series of models of increasing complexity [23]. The basic model consists of only the He + 1s state, which we call 1T (1 True state).…”

“…We also assess which form offers the most numerically stable method, particularly when used with a limited multielectron basis set. Studies assessing the propagation of the wavefunction have demonstrated that to obtain the most accurate results for a limited basis in the TDRM approach the laser field is best described in the dipole length gauge [23]. On the other hand, timepropagation in SAE calculations is commonly performed by describing the laser field in the velocity gauge.…”

“…Helium is chosen for three reasons. Firstly, the simple structure allows for the systematic varying of the multielectron basis functions, the impact of which has been assessed for TDRM in terms of photoionization [23], but not for HG. Secondly, the absence of a closed core simplifies the calculation of dipole acceleration matrix elements, and hence we can compare spectra in all three forms.…”