Hyperfine and Zeeman interactions in ultracold collisions of molecular hydrogen with atomic lithium

We present a rigorous quantum scattering study of the effects of hyperfine and Zeeman interactions on cold Li - H$_{2}$ collisions in the presence of an external magnetic field using a recent ab initio potential energy surface. We find that the low-field-seeking states of H$_{2}$ predominantly undergo elastic collisions: the ratio of elastic-to-inelastic collisions exceeds 100 for collision energies below 1.5 K. Furthermore, we demonstrate that most inelastic collisions conserve the space-fixed projection of the nuclear spin. We show that the anisotropic hyperfine interaction between the nuclear spin of H$_{2}$ and the electron spin of Li can have a significant effect on inelastic scattering in the ultracold regime, as it mediates two processes: the electron spin relaxation in lithium, and the nuclear spin - electron spin exchange. Given the predominance of elastic collisions and the propensity of inelastic collisions to retain H$_{2}$ in its low-field-seeking states, our results open up the possibility of sympathetic cooling of molecular hydrogen by atomic lithium, paving the way for future exploration of ultracold collisions and high-precision spectroscopy of H$_{2}$ molecules.