The time-dependent surface flux (t-SURFF) method is introduced for computing strong-field infrared (IR) photo-ionization spectra of atoms by numerically solving the time-dependent Schrödinger equation on minimal simulation volumes. The volumes only need to accommodate the electron quiver motion and the relevant range of the atomic binding potential. Spectra are computed from the electron flux through a surface, beyond which the outgoing flux is absorbed by infinite range exterior complex scaling (irECS). Highly accurate IR photo-electron spectra are calculated in single active electron approximation and compared to the literature results. Detailed numerical evidence for performance and accuracy is given. Extensions to multi-electron systems and double ionization are discussed.

We show how to combine finite elements and the discrete variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of H + 2 , as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.

Our previously developed finite-element/ discrete variable representation in prolate spheroidal coordinates is extended to two-electron systems with a study of double ionization of H2 with fixednuclei. Particular attention is paid to the development of fast and accurate methods for treating the electron-electron interaction. The use of exterior complex scaling in the implementation offers a simple way of enforcing Coulomb boundary conditions for the electronic double continuum. While the angular distributions calculated in this study are found to be completely consistent with our earlier treatments that employed single-center expansions in spherical coordinates, we find that the magnitude of the integrated cross sections are sensitive to small changes in the initial-state wave function. The present formulation offers significant advantages with respect to convergence and efficiency and opens the way to calculations on more complicated diatomic targets.