Calculating differential cross sections for electron-impact ionization without explicit use of the asymptotic form

We describe the calculation of singly differential (energy-sharing) cross sections for electron-impact ionization. First, using exterior complex scaling, we calculate the outgoing portion of the scattering wave function without explicit use of asymptotic boundary conditions. Once that wave function is known for a finite region of space, the outgoing flux can be calculated and extrapolated to large distances according to behavior that is specific to the ionization problem. The differential cross section is proportional to the outgoing flux in specific directions of a hyperspherical angle in the coordinates. Calculations on the singlet s-wave radial limit (Temkin-Poet and collinear) models of electron-hydrogen atom ionization are presented. {copyright} {ital 1997} {ital The American Physical Society}