Magnetically quantized continuum distorted waves

A new derivation of continuum distorted-wave theory is presented. It is generalized to magnetically quantized continuum distorted waves. The context is analytic continuation of hydrogenic-state wave functions from below to above threshold, using parabolic coordinates and quantum numbers including m the magnetic quantum number. This continuation applies to excitation, charge transfer, ionization, and double and hybrid events for both light- and heavy-particle collisions. It is applied to the calculation of double-differential cross sections for the single ionization of the hydrogen atom and for a hydrogen molecule by a proton for electrons ejected in the forward direction at a collision energy of 50 keV and 100 keV respectively.