Small-angle scattering of ions or atoms by atomic hydrogen

A theory for small-angle scattering of arbitrary medium- or high-energy atoms or ions by atomic hydrogen is described. Results are obtained in terms of the known closed-form and easily calculable Glauber-approximation scattering amplitudes for electron-hydrogen collisions and for collisions between the nucleus (treated as one charged particle) of the ion or atom and the hydrogen atom, and in terms of the transition form factor of the arbitrary ion or atom. Applications are made to the angular differential cross sections for the excitation of atomic hydrogen to its $n=2\mathrm{}$ states by singly charged ground-state helium ions having velocities of roughly between ½ and 1 a.u. The differential cross sections are obtained in terms of electron-hydrogen amplitudes and the known ${\mathrm{He}}^{+}$ ground-state form factor. Comparisons are made with other calculations and with recent measurements. The results are in good agreement with the data. It is seen that the effect of the ${\mathrm{He}}^{+}$ electron is to produce significant constructive interference at most energies.