Cross sections for inelastic electron-ion scattering in weak-coupling approximations

Coulomb-Born and distorted-wave theories for electron-ion scattering are described and applied to several transitions in H-, He-, Li-, and Be-like isoelectronic ions. A number of options are available in these theories and the numerical data plus theoretical arguments are used to define the most accurate alternative. The most complex of these weak-coupling approaches (DWXII) which is a distorted-wave theory that includes initial- and final-state distorting potentials, local-exchange approximations to the exchange terms appearing in the distorting potentials, the retention of the full distorting potential in the S-matrix element one-electron exchange term, and S-matrix elements transformed to guarantee a unitary S matrix, is recommended as a survey tool with the potential for reasonable accuracy. Supporting evidence becomes stronger for increasing charge on the ion. The sum of cross sections for the excitation of nearly degenerate or strongly coupled states remains reliable for examples that exhibit the expected weak-coupling inaccuracies in predicting the individual contributions. The long-recognized requirement of using accurate target wave functions, including configuration interaction, is reemphasized.