LETTER TO THE EDITOR On the validity of the impulse approximation for electron capture in asymmetric collisions

Abstract. For electron capture in asymmetric ion-atom collisions the projectile-target charge ratio is a natural expansion parameter. Recently Macek and Taulbjerg have claimed that the anomalies of the Coulomb T matrix introduce corrections to the impulse approxi-mation which do not depend on this ratio. We show that this is due to the approximations they introduced, and that more accurate estimates lead to a dependence of their correction on the charge asymmetry. This correction may nevertheless be important even for rather asymmetric systems. The problem of electron capture in asymmetric ion-atom collisions has received some attention lately, as it has become clear that this process may, after all, be quite well described by perturbation theory. If one carries out a systematic expansion of the scattering amplitude to the first order in the weaker of the two nuclear fields, retaining the stronger potential to all orders and also preserving the correct asymptotic behaviour of the initial- and final-state wavefunctions, one arrives at the so called ‘second-order’ Coulomb-Born (CB) approximation of Macek and Shakeshaft (1980). (The cor-responding ‘first-order ’ amplitude in their approach, which is the Brinkman-Kramers amplitude, is actually cancelled by a ‘second-order ’ contribution.) If we consider the transfer from a heavy target (with charge 2 2) to a light projectile (charge (Z I) , the transfer amplitude can be written as an overlap between the matrix element for the target excitation to an intermediate off-shell continuum state and the (travelling) projectile final-state wavefunction. Since the amount the continuum state is off shell is proportional to the weaker potential, it is apparently consistent to replace the off-shell state by an on-shell one, which leads to the impulse approximation (IA) (McDowel