Critical test of first-order theories for electron transfer in collisions between multicharged ions and atomic hydrogen: The boundary condition problem

We have thoroughly investigated electron capture from a hydrogen atom by bare nuclei at intermediate and high energies. The first Born approximation with and without correct boundary conditions is used to compute total cross sections. Both methods possess the same perturbation potential for the reaction under study. The only difference is in the logarithmic phase distortion of the exit channel state due to the long-range Coulomb interaction between the two aggregates. Evidence is presented which substantiates that these Coulomb phases for the relative motion of heavy particles are of paramount importance for an adequate description of charge exchange. The standard Jackson-Schiff approximation which does not consider the boundary condition problem fails completely in comparison with the measurement. In contrast, the first Born approximation with the correct boundary conditions, which takes the asymptotic Coulomb effect into full account, is found to be systematically in excellent agreement with the experimental data for values of the projectile charge ranging from 1 to 6.