Quantum pairing of impurities in quantum crystals

We calculated the time of pairing by quantum diffusion of ortho-${\mathrm{H}}_{2}$ impurities in solid para-${\mathrm{H}}_{2}$. The important feature of the pairing process is a strong directional bias associated with the dependence of the hopping rates on energy mismatches caused by the interaction of the pairing particles. This bias at moderate temperatures is against a mutual approach of particles and creates a ``kinetic barrier.'' At lower temperatures, the corresponding diffusion mechanism freezes out, which leads to a rapid increase in pairing rates. This explains a well-developed, experimentally observed maximum in the pairing time as a function of temperature: a maximum that exists in spite of a monotonic temperature dependence of individual hopping rates. Our results are in good agreement with experimental data.