Electron-impact ionization of Ne and Ar in the eikonal and Born approximations

Utilizing the first Born approximation and an eikonal/closure approximation plus Bethe's generalized-oscillator-strength (GOS) formalism, we evaluate $s$- and $p$-shell ionization of Ne and Ar. Partial-wave contributions to the GOS are calculated using an analytic independent-particle model (IPM) whose parameters have been established in previous work on excitation GOS's. For single ionization of Ne and Ar shells ($K$ shell excepted), total cross sections and cross sections differential in the energy of the secondary electron are calculated for electron-impact energies near threshold to 10 keV. The eikonal/closure approximation which is developed in detail for large atoms differs from the Glauber theory by not assuming sudden passage of the projectile in which the time dependence of the bound electron and the energy transfer to the projectile may be neglected. In the single-scattering limit, the theory produces a simple factor multiplying the usual Born approximation amplitude, which leads to improved agreement with experiment at low energy.