Theory of Elastic Differential Scattering in Low-EnergyHe++He Collisions

The elastic differential scattering of ${\mathrm{He}}^{+}$ in He is calculated at the barycentric energies 15, 50, and 300 eV for comparison with the experiments of Lorents and Aberth (preceding paper). We use available computed potentials of the $g$ and $u$ states of ${\mathrm{He}}_2^{+}$ dissociating smoothly to ground-state ${\mathrm{He}}^{+}$+He. The quantal interference pattern is reproduced by applying the principle of superposition to the classical scattering amplitudes appropriate to the pure $g$ and $u$ states, i.e., amplitudes whose magnitudes and phases are given by classical integrals over the trajectories corresponding to the $g$ and $u$ potentials separately. The interference takes place at the common angle $\theta$, and usually involves different values of the angular momentum in the 2 states. Nonzero minima occur even in 2-state elastic scattering because the 2 interfering terms may differ in magnitude. A secondary interference at large angles is identified as an effect of nuclear symmetry that should disappear in an experiment using 2 different isotopes. The 2-state theory appears able to account quantiatively for the 5 principal features of the experimental elastic scattering: the upper and lower envelopes, the rainbow scattering, and the primary and secondary oscillations. For further improvement in detail, better information is needed on the behavior of the potentials at large and small internuclear distance. At large angles and high energies the experimental upper envelope falls below the elastic 2-state theory. This discrepancy is probably due in part to losses into inelastic channels.