Close-Coupling Theory of Ionization: Successes and Failures

We suggest that the close-coupling (CC) approach to ionization requires an infinite expansion of square-integrable pseudostates to completely solve the $e-\mathrm{H}$ three-body breakup problem. The slow convergence is due to the fact that the single-differential cross section, arising in CC calculations, should have a step at the point where the two outgoing electrons have the same energy. However, all discrete transitions, including total ionization, as well as angular differential ionization profiles, are able to be described accurately in calculations using relatively small finite expansions of the total wave function.