Inner-shell charge transfer in asymmetric ion-atom collisions

A method used previously for inner-shell ionization in asymmetric ion-atom collisions is extended to include charge transfer between the target inner shells and projectile $K$ shell. We work in the energy range ${\eta }^{\frac{1}{2}}=\frac{\hslash v}{Z_N{e}^2}\lesssim 1$ and use an independent-electron model (Hartree-Fock) for the target. We treat the interaction with the projectile as a time-dependent perturbation due to a bare charge moving on a straight-line path. Our method, as for ionization, is very efficient in that with our target-centered expansion of the system wave function, all requisite matrix elements needed at a particular projectile energy are pretabulated and used at all impact parameters. A critical feature of our results is the recognition of the importance of target continuum states of energy approximately equal to the kinetic energy (in the target frame) of the electron on the projectile, and the development of a method to properly include such resonance states in our pseudostate calculation. We present selected numerical results to illustrate our method and to demonstrate the projectile energy and nuclear charge dependence of the cross sections. A general feature of the results presented is that the computed cross sections are of the order of 0.3-0.5 times the Brinkman-Kramers estimate. Simultaneously, we also compute cross sections for electron stripping of the projectile, and find them to be dominated by transitions to the above-described resonant continuum state of the target.