Elastic Differential Scattering of Low-Energy H+ by Rare-Gas Atoms

Elastic scattering experiments have been performed on the systems ${\mathrm{H}}^{+}$ + Kr, ${\mathrm{H}}^{+}$ + Ar, ${\mathrm{H}}^{+}$ + Ne, and ${\mathrm{H}}^{+}$ + He with collision energies between 3 and 60 eV. For each of the above systems the experimental differential cross section $\ensuremath{\sigma}(\ensuremath{\theta})$ at one of the lower energies (typically 4 or 6 eV) has been compared with the results of a partial-wave calculation where the JWKB method was used to find the phase shifts and consequently the differential cross section. For the systems Kr${\mathrm{H}}^{+}$, Ne${\mathrm{H}}^{+}$, and Ar${\mathrm{H}}^{+}$an analyticalform was chosen for $V(r)$, and parameters (e.g., the well depth $U$ and the value ${r}_{m}$ of the internuclear separation for which the potential is a minimum) in this model were varied until the calculated $\ensuremath{\sigma}(\ensuremath{\theta})$ agreed quite well with the experimental results. In the case of ${\mathrm{H}}^{+}$ + He two ab initio calculations of the interatomic potential $V(r)$ are available, and each has been used in the JWKB expression to determine the differential cross section. For one of the potentials the predicted $\ensuremath{\sigma}(\ensuremath{\theta})$ is in striking agreement with the experiment. This method is seen, therefore, to provide a sensitive test of such calculations when they exist.