a Theoretical Analysis of Excitation and Charge Exchange in Ion-Atom Collisions.

The impact parameter dependence of the excitation and charge transfer process for the simple model of a collision between a bare nucleus and a one-electron nonrelativistic hydrogenic atom has been examined and calculated. Using semiclassical collision theory, Kepler motion on a hyperbolic trajectory is chosen to describe the relative nuclear motion. Applying a variational principle, coupled differential equations are derived for the amplitudes of the electronic states. Because of the Kepler motion, including recoil of the target, a general transformation theory connecting inertial and non -inertial frames of reference has been developed to obtain the appropriate Hamiltonian and wave functions. Fast Fourier transform and Romberg algorithms are applied to evaluate the matrix elements. The GEARS method has been used to solve the coupled differential equations. A preliminary calculation has been performed to evaluate the excitation and charge exchange probabilities.