Hyperfine and Zeeman interactions in ultracold collisions of molecular hydrogen with Li atoms

Cold collisions involving molecular hydrogen (H₂) have been the subject of significant interest across various contexts, from astrochemistry of the interstellar medium to controlled chemistry at extremely low temperatures. However, previous theoretical studies of such collisions neglected the effects of hyperfine interactions and Zeeman shifts, which could be substantial at ultracold conditions (the hyperfine structure of ortho-H₂ in the first rotational state is on the order of 20 μK).

We present a rigorous quantum scattering study of the effects of hyperfine and Zeeman interactions on cold Li-H₂ collisions in the presence of an external magnetic field using a recent ab initio potential energy surface. We obtain a favorable ratio of the cross sections for elastic to inelastic collisions for the low-field-seeking Zeeman states of H₂. We discuss the importance of the spin-dependent Li-H₂ interaction, the role of collisions conserving the projection of the total nuclear spin of H₂, and the implications for sympathetic cooling of molecular hydrogen by lithium in a magnetic trap.