Complete numerical solution of electron-hydrogen model collision problem above the ionization threshold

Benchmark results are presented for electrons colliding with hydrogen atoms in the S-wave (Temkin-Poet) model collision problem, which neglects angular momentum. Complete results (elastic, inelastic, and ionization), accurate to 1%, are obtained by numerically integrating Schrodinger's equation subject to correct asymptotic boundary conditions. This marks the first time direct matching to asymptotic boundary conditions has been shown to yield convergent ionization amplitudes for a Coulomb three-body problem. Results are presented for impact energies of 54.4 and 40.8 eV, where comparison with other theories is available.