Second Born Approximation for Charge Exchange with Correct Boundary Conditions

The second Born approximation for charge exchange with correct boundary conditions is formulated for completely stripped projectiles impinging on hydrogenlike atomic systems. The theory employs the free-particle Green's function G 0 + as an intermediate propagator. The usual channel states are distorted by appropriate inclusion of the logarithmic Coulomb phase factors which are consistent with the perturbation potentials. The present method is computationally very attractive. In particular, the transition amplitude for a general homonuclear case was obtained as a combination of two-dimensional integrals with smooth integrands. In an illustrative computation, good agreement is found between the proposed second Born approximation and the recent experimental differential cross-sections of Martin et al. and Vogt et al. on the most fundamental proton-atomic hydrogen charge exchange.