Use of two-body close-coupling formalisms to calculate three-body breakup cross sections

We analyze the consequences of discretizing one of the two continua in three-body breakup to reduce it to a two-body close-coupling problem. We identify the origin of oscillations in the singly differential cross section in those {open_quotes}convergent close-coupling{close_quotes} calculations as lying only in the way the cross section is calculated from the wave function and not in the wave function itself. The anomalous {open_quotes}step-function{close_quotes} behavior of those calculations is derived from a stationary-phase argument. Calculations are presented on the Temkin-Poet model for electron-impact ionization of hydrogen, a breakup problem with exponential potentials, and an analytically solvable model. The anomalies associated with two-body close-coupling calculations are demonstrated using wave functions from complex exterior scaling calculations that otherwise give converged results without any anomalies. {copyright} {ital 1999} {ital The American Physical Society}