Model for High-Energy Charge Transfer

A one-dimensional model of charge transfer is solved numerically, and the results are compared with standard approximation techniques. At higher energies, a regularity in the phase of the numerical result can be derived by an approximation procedure which in lowest order is the eikonal approximation. This approximation is applied to the problem of charge transfer in proton-hydrogen collisions. The result falls below the usual Born approximation; the limiting value at high energies is $\frac{23}{48}$ of the usual Born (Brinkman-Kramers) result. The approximation is also applied to the problem of excitation of atoms by fast protons. The result is an energy-dependent multiple of the Born approximation. The multiplier slowly approaches unity at high energy. A discussion of previous theoretical work relevant to high-energy rearrangement collisions is also presented.