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We present results for the electron impact ionization of a sequence of hydrogenic ions and the first five ions in the He isoelectronic sequence. These are obtained in coplanar symmetric geometry for a wide range of energies, from near threshold into the intermediate range.We have concentrated the analysis on the role of the ion in the incident and final channel. All calculations are performed in a distorted-wave Born approximation (DWBA) which allows for elastic scattering in both the incident and final channels. The role of repulsion between the final state electrons is discussed in a simple model. Comparisons are also shown with DWBA calculations that include a polarization potential, and with a Coulomb-Born approximation.

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We develop a method for the reconstruction of a perfectly reflecting rough surface from phaseless measurements of a field arising from single frequency scattering at grazing angles. Formulations are given for both Dirichlet and Neumann boundary conditions, and numerical experiments are presented in which close agreement is found with the exact solution. The approach is a marching method based on the parabolic integral equation, which recovers the surface progressively in range, and is iterated a small number of times to produce the final result. It is found that the approach is robust with respect to spatially localized perturbations and to measurement noise.

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