Deflection effects and charge transfer in inner-shell vacancy production

A method used in the calculation of inner shell ionization in asymmetric ion-atom collisions is extended to include projectile deflection effects and charge transfer to the projectile. Work is done in an independent electron model (Hartree-Fock) for the target, and the interaction is treated with the projectile as a time-dependent perturbation of the system. It is shown tht the time-dependent problem can be solved for the projectile moving along the classical hyperbolic trajectory that results from the nuclear repulsion. The method is very efficient due to the utilization the target-centered expansion of the system wave function. This means that all the required matrix elements can be pretabulated and are then available for use at all impact parameters. The method is first applied to the impact-parameter dependence of K-shell ionization by protons incident upon copper in the energy range 0.5 to 2 MeV. Excellent agreement with the experiments of Andersen et al., is found at the lower energy. Less satisfactory agreement is obtained in the higher energy region. Next the projectile is considered to move in a straight line path with constant velocity, and extend the method to include charge transfer between the target inner shells and the K-shell of the projectile. A critical feature of the 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. An approach is developed to properly include such resonance states in our pseudostate calculation. Selected numerical results are presented to illustrate the method and to demonstrate the projectile energy and nuclear charge dependence of the charge transfer cross sections