Determination of the H-He Potential from Molecular-Beam Experiments

Absolute total cross sections for D-He scattering were measured with an accuracy of 1% at 0.3, 0.5, and 0.6 eV. These new data were combined with published relative measurements of the velocity dependence of the H-He cross section in a χ² minimalization procedure. The resulting potential $V(R)$ as function of internuclear separation R is precisely determined in the repulsive range 1.7<R<R₀ with V(R₀)=0. Several multiparameter potential models were tried. Of these the four-parameter ansatz V(R)=A(e^-αR-e^-αR₀) (for R<R₀)=4ε[(R₀R)¹²-(R₀R)⁶] (for R>R₀) was found to describe the data best. Parameters obtained are $A=70.00$ eV, α=3.383 ^-1, R₀=3.20 {}, and ε=0.39 meV. The well depth ε, to which the measurements are insensitive, is chosen to match the theoretical van der Waals constant C₆=2.83 a. u. The potential is compared with results of ab initio calculations, and a probable ε range is discussed. For 0.35ε0.70 meV the calculated low-energy cross section shows a pronounced Ramsauer-Townsend minimum. The possibility of its observation is pointed out.