Recent developments in the theory of electron-ion collisions

Until a few years ago, calculations for electron scattering from atoms and ions were typically performed using non-perturbative close-coupling-type approximations for low impact energies and perturbative Born-type methods in the high-energy regime. Especially for singly and doubly ionized targets, however, neither one of those methods is particularly reliable for the "intermediate energy regime", i.e., impact energies near and up to about five times the ionization threshold. This gap has recently been closed by the convergent close-coupling (CCC), the R-Matrix with pseudo-states (RMPS), the intermediate-energy R-matrix (IERM), and time-dependent lattice methods. The principal ideas behind these approaches are introduced and some example cases, illustrating the need for using such sophisticated approaches, are discussed.