Approach to electron-impact ionization that avoids the three-body Coulomb asymptotic form

We propose a general approach to the electron-impact ionization problem that involves two distinct steps. First, using exterior complex scaling, we calculate the outgoing portion of the scattering wave function without explicit use of boundary conditions for ionization or any other channel. Once that wave function is known for a finite region of space, we make use of a general formula for extracting the integral cross section for the breakup process from any wave function. That formula is a projected form of the optical theorem and has no relation to complex coordinates or other methods of computing the scattering wave function. A preliminary calculation on the $s$-wave radial limit form of electron–hydrogen-atom ionization is presented in excellent agreement with calculations by other approaches.