Inversion Problem for Ion-Atom Differential Elastic Scattering

An inversion procedure to recover the intermolecular potentials from low-energy (4-14 eV) differential scattering data for the systems HeH⁺, NeH⁺, ArH⁺, and KrH⁺ is presented. The first step in this procedure is to construct the phase shifts {η(l)} from the experimental differential cross section σ(θ) and, for reasons of intuition, the corresponding classical deflection function. This is accomplished by employing a new technique developed recently by Remler which involves singularities in the S matrix. The Remler method is as accurate as, but less cumbersome than, the frequently employed standard partial-wave sum and in addition leads to an intuitive connection between η(l) and σ(θ). Having found {η(l)}, the intermolecular potential may be determined by means of the transformation method of Vollmer. To test the entire inversion procedure, the intermolecular potential obtained from the H⁺ + He scattering data is compared to the ab initio calculation by Wolniewicz of the ground-state potential for HeH⁺. This method should be applicable to any spherically symmetric scattering system.