Time-dependent approach to collisional ionization using exterior complex scaling

We present a time-dependent formulation of the exterior complex scaling method that has previously been used to treat electron-impact ionization of the hydrogen atom accurately at low energies. The time-dependent approach solves a driven Schr\"odinger equation, and scales more favorably with the number of electrons than the original formulation. The method is demonstrated in calculations for breakup processes in two dimensions (2D) and three dimensions for systems involving short-range potentials and in 2D for electron-impact ionization in the Temkin-Poet model for electron-hydrogen atom collisions.