Analytically continued generalized continuum distorted waves

The continuum distorted-wave eikonal-initial-state (CDW-EIS) theory of Crothers and McCann (Crothers D S F and McCann J F 1983 J. Phys. B: At. Mol. Phys. 16 3229) used to describe ionization in ion–atom collisions is generalized (G) to GCDW-EIS, to incorporate the azimuthal angle dependence into the final-state wavefunction. This is accomplished by the analytic continuation of hydrogenic-like wavefunctions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 keV u−1, the total CDW-EIS ionization cross section falls off, with decreasing energy, too quickly in comparison with experimental data by Crothers and McCann. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment, by including contributions from non-zero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it.