Interaction Potentials from the Velocity Dependence of Total Atom-Atom Scattering Cross Sections

Abstract

Methods are described which yield the interatomic potential energy parameters from the velocity ($v$) dependence of the total scattering cross section ($Q$). These are applied to previously reported measurements of the scattering of lithium by the rare gases. The Lennard-Jones (12,6) potential is assumed. The cross sections for scattering by argon, krypton, and xenon had been measured in a "low-energy" region, where $Q\left(v\right)\mathrm{}$ is undulatory. From the extrema velocities the product $\epsilon \sigma$ may be obtained, where $\epsilon$ is the depth of the interatomic potential well and $\sigma$ is the interatomic separation at the zero of potential energy. From the absolute value of $Q$, the parameter $\sigma$ (and thus $\epsilon$) may be determined separately. These quantities were also deduced (although less accurately) for the scattering by helium and neon, which were studied in the "high-energy" region. Using the "experimental" $\epsilon$ and $\sigma$, theoretical curves of $Q\left(v\right)\mathrm{}$, calculated by a partial-wave analysis, agree well with the experimental results. A minimum to the number of diatom bound states was also established.