One and a half centered expansion for ion-atom collisions

Fast ion-atom collisions in which charge transfer plays a dominant role have been traditionally treated by a two center expansion (TCE): the state wavefunction is approximated by a truncated set of Hilbert states centered on the target and projectile. This method is accurate but expensive in the use of computer time. A new method which allows charge transfer through variational time independent amplitudes, and target excitation and ionization through variational time dependent amplitudes is presented. The method retains the efficiency of a single centered expansion and yet reproduces the conventional TCE results in situations where charge transfer is dominant. Comparison to experiment is made