Target continuum distorted-wave theory for capture of inner-shell electrons by fully stripped ions

The target continuum distorted wave (TCDW) theory is derived and developed. It describes charge exchange in asymmetric collisions, in particular the collision of a projectile ion of low charge with a target ion of high charge. The final state is represented by a TCDW function. The initial state is taken as a travelling atomic orbital, while the intermediate states are represented by a Coulomb-Green function. The theory is applied to capture by protons from the inner shells of heavy atoms. For s-s transitions, it is found that within a standard on-shell full-peaking approximation the second-order amplitude does not contribute. The total cross section for K-K electron capture in proton-carbon, neon and argon atom collisions is calculated in the energy range corresponding to values of Z T /v from 0.5 to 3.0, where Z T is the nuclear charge of the target and v the velocity of impact in atomic units. Agreement with experiment is excellent in all three cases and the cross section values compare extremely favourably with those of the well known strong-potential Born theory.