First and second Born calculations of (e, 2e) excitation-ionization of helium

We report detailed calculations of the first Born triple-differential cross section for (e, 2e) excitation-ionization of ground state He to He⁺ (n = 2). These are in accord with the very recent work of Kheifets et al (1999 J. Phys. B: At. Mol. Opt. Phys. 32 L433) and confirm that the first Born amplitude is now known very accurately. We illustrate the sensitivity of the first Born cross section to the choice of initial and final state wavefunctions. We combine our accurate first Born amplitude with an estimate of the second Born term evaluated in the closure approximation. As in previous work (Marchalant et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 1141) we find that second-order effects are significant even up to energies as high as 5.5 keV. Agreement with experiment generally remains not very satisfactory.