Reformulated impulse approximation (RIA) for charge exchange in fast ion-atom collisions

The problem of charge exchange in fast collisions of completely stripped projectiles with hydrogen-like atoms is theoretically investigated with the impulse hypothesis. The standard single-centre impulse approximation (IA) is substantially revised. The framework of two-centre scattering is explored to consistently formulate the problem with full respect of the exact boundary conditions to the complete state vectors in both entrance and exit channels. This is achieved by simultaneously introducing intermediate states for an attractive and a repulsive Coulomb potential with the same interaction strength. The difference between these potentials, which are present in the main dynamic equation for the two-centre continuum states, reduces to a short-range interaction at large distances. As a consequence, the resulting double continua, which originate from the action of a two-potential Moller wave operator onto three-particle intermediate plane waves, exist in a mathematically rigorous manner. This is strictly required by the formal scattering theory. In addition, the present model, termed the reformulated impulse approximation (RIA), includes multiple scattering effects, which are completely discarded in the standard IA. As an illustration of the proposed theory, differential and total cross-sections are computed for electron capture by a proton from an atomic hydrogen at impact energies ranging from 20 to 7500 keV. Significant improvement over the IA is obtained. The IA severely underestimates the experimental data on total cross-sections in the range 20-350 keV, whereas the RIA is in very good agreement with the measurements at all the energies under study. Moreover, the IA completely fails to reproduce the experimental differential cross-sections at intermediate energies 25, 60 and 125 at which the RIA is very successful. Also at high energies such as 2, 2.8, 3 and 5 MeV, where Thomas double scattering enriches the angular distribution of scattered projectiles, the RIA is in much better agreement with the measurements than the IA.