Anisotropies in the distribution of electrons captured to continuum states of a fast moving charge

The author considers the second-order Born approximation for a charge transfer process to study electron capture to continuum states of a fast bare charge after a collision with a hydrogenic atom. By relaxing usual approximations, he is able to take full account of the corrections to the nu -12 asymptotic behaviour of the cross section with impact velocity nu , and consequently to obtain the angular dependence of the electron distribution around the projectile. There is a dominating nu -14 ln nu anisotropic term, which is due to a contribution to the transition amplitude coming from the neighbourhood of the pole in the free-particles Green's propagator. The large value of the corrections to the nu -12 dependence of the cross section casts doubts on the validity of such asymptotic expansions for non-relativistic velocities.