Analytic Continuation: Continuum Distorted Waves

The continuum distorted-wave eikonal initial-state (CDW-EIS) approximation is reviewed and two-centre effects such as the saddle-point mechanism discussed. The continuum distorted-wave theory is then generalized such that the azimuthal angle dependence is factored into the final state. This is achieved by the analytic continuation of hydrogenic-state wave functions from below to above threshold, using parabolic coordinates and magnetic quantum numbers, thus providing a more complete set of states. Double differential cross sections are considered for the single ionization of a H atom and molecule, ejected in the forward direction at a collision impact energy of 40 keV and 100 keV respectively.