Quantum tunneling and motional narrowing of HD NMR line shapes in solid hcpH2

The observed narrowing of the NMR line shapes of HD impurities in solid parahydrogen is interpreted in terms of a motional narrowing effect due to quantum tunneling. This model is successful in describing the dependence of the HD linewidths on the orthohydrogen concentration (0.1-4 at.%) and predicts a tunneling frequency $J\sim 1$ kHz. This value can be understood in terms of current views of tunneling in quantum solids which predict that three-body cyclic permutations dominate the tunneling processes in hcp ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${\mathrm{H}}_2$. Estimates of the tunneling frequencies to be expected for ${\mathrm{H}}_2$ based on the experimental values for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are in close agreement with those needed to explain the NMR results.