Channel-distorted Brinkman-Kramers approximation for ionization by highly-charged ion impact

We have analysed the capture-to-continuum aspects of the ionization process in ion-atom collisions in a channel-distorted, first-order approximation. In contrast to the standard Brinkman-Kramers approximation, we have found that the channel-distorted version correctly reproduces the ionization amplitude derived in a quasi-elastic scattering model for electrons in the binary-encounter-peak region of the ionized electron spectrum. Clearly, the first-order approach misses the double-scattering contribution, known to play a significant role at the cusp of electrons travelling with approximately the same velocity as the projectile, but our analysis is interesting in this region too, since it shows that the single-collision part of the cusp amplitude depends strongly upon the high-momentum tail of the Compton profile of the initial electron state, a feature that should receive more attention in future evaluations of higher-order theories. The present calculations are tested against experimental data in the binary-encounter region. Quantum effects due to binding in the initial state are isolated in a generalized off-energy-shell factor. This factor approaches unity at the centre of the binary peak, but appears to shift the position of the peak and to change its shape. The theoretical shift is in reasonable accord with the experimental data, but it is concluded that further work is needed, with special emphasis on the validity of the single-particle model and the corresponding representation of the initial state of the target atom.