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Abstract

We consider hydrogen and helium ionization with emission of soft electrons in high-velocity collisions with bare ions in the perturbative regime |Zp|/vp < 0.1, where Zp is the projectile charge and vp the collision velocity. For such collisions it is usually assumed that the first-order approximation in the projectile–target interaction yields good results for single ionization. However, by performing calculations in the first and second Born, Glauber and CDW–EIS approximations, we show that higher-order effects can considerably influence electron emission already in the collision plane where the main part of the emission occurs. Moreover, the deviations from the first-order results become even stronger if the electron emission is analysed in the plane perpendicular to the momentum transfer. In this plane a pronounced structure appears in the fully differential cross section. This structure is different for collisions with Zp > 0 and Zp < 0 and the difference remains noticeable even for collisions with protons and anti-protons moving at velocities approaching the speed of light. It is also found that, on average, the higher-order effects are relatively more important for collisions with negatively charged projectiles. The deviations from first-order results for emission from hydrogen in the perturbative regime are attributed mainly to the projectile interaction with the hydrogen nucleus. In case of helium single ionization, our calculations suggest that a proper description of electron emission in the perpendicular plane may be very demanding with respect to the quality of the approximations for the initial and final helium states.