Unified treatment of slow atom-atom and ion-atom collisions

A unified treatment of slow ion-atom and atom-atom collisions for many-electron systems is proposed. The time-dependent electronic wave function is expanded in terms of traveling atomic orbitals of the two collision centers at large internuclear separations and is matched to the solution in the inner region where it is expanded in terms of molecular orbitals without translational factors. It is shown that this method avoids the difficulties associated with the conventional perturbed-stationary-state approximation. Application to charge transfer in the ${\mathrm{H}}^{+}$+${\mathrm{He}}^{+}$ collision is illustrated.