Elastic Differential Scattering of Low-EnergyH+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 $\sigma \left(\theta \right)$ 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 $V\left(r\right)\mathrm{}$, 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 $\sigma \left(\theta \right)$ agreed quite well with the experimental results. In the case of ${\mathrm{H}}^{+}$ + He two ab initio calculations of the interatomic potential $V\left(r\right)\mathrm{}$ are available, and each has been used in the JWKB expression to determine the differential cross section. For one of the potentials the predicted $\sigma \left(\theta \right)$ is in striking agreement with the experiment. This method is seen, therefore, to provide a sensitive test of such calculations when they exist.