Interaction potential of the H-He system and the hyperfine frequency shift of H in He buffer gas

The van der Waals potential of the H-He interaction and the hyperfine frequency shift of H in He are predicted using the Tang-Toennies model. This model damps the long-range ab initio dispersion terms individually using a universal damping function and adds to this a simple Born-Mayer repulsive term. The Born-Mayer parameters are derived from self-consistent-field calculations. The resulting potential is found to be in good agreement with two molecular-beam experiments and its well parameters, in excellent agreement with the complete configuration-interaction calculation. In order to compare with experiment, the hyperfine frequency shift is thermally averaged over the potential both quantum mechanically and classically. The thermally averaged results are in excellent agreement with experiment in the high-temperature range but there are some discrepancies with the measurements at 0.5 and at 1.15 K. These discrepancies may be due to the fact that the long-range coefficient ${\mathit{K}}_{10}$ used is too small. The quantum and classical results are practically identical for temperature above 40 K. The classical statistics fails completely only for temperature below 5 K. Also in the quantum calculation, the isotope effect between ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is found to show up only for temperature below 10 K. The theoretical isotope effect is in qualitative agreement with experiment.