Inner-shell charge transfer in a distorted-wave eikonal approximation using the asymptotic interaction

$K$-shell charge-transfer cross sections are calculated for swift fully stripped ions impinging on target atoms in a post-interaction distorted-wave formalism. The projectile interaction with the residual target atom is part of the unperturbed Hamiltonian, and is approximated by its asymptotic form while the consequent projectile distortion is approximated by an eikonal wave function. The results are compared to experiment and to other theoretical calculations and are used to shed light on some aspects of the three-body Coulombic rearrangement process and in particular on the significance of asymptotic properties of interactions and wave functions on the results of simple approximation schemes.