Application of the time-dependent close-coupling approach to few-body atomic and molecular ionizing collisions

We review the recent progress made in applying the time-dependent close-coupling approach to ionizing collisions of electrons, photons, and ions with small atoms and molecules. The last twenty years have seen a proliferation of non-perturbative approaches applied to fundamental atomic and molecular scattering processes. Such processes form the building blocks of describing the dynamics of plasmas over a wide range of temperatures and densities, and also provide insight into the long-range Coulomb interactions between charged particles. Studies of the few-body Coulomb problem presented in electron, photon, or ion-impact ionization of small atoms and molecules, by direct solution of the time-dependent Schrödinger equation, are particularly useful because the complicated three-body boundary conditions of more than one continuum particle in a Coulomb potential are not required. With the continuing growth and increasing availability of high-performance computing resources, such methods can now be applied to a wide variety of scattering processes. The recent progress made using such a time-dependent approach is described in this colloquium. In this paper, we focus on the recent results obtained for one-, two-, and three-electron systems, thus building on a previous review of the time-dependent close-coupling method [M.S. Pindzola et al., J. Phys. B 40, R39 (2007)], which also described the application to multi-electron targets