Nuclear Spin Relaxation in Cold Atom-Molecule Collisions

We explore the quantum dynamics of nuclear spin relaxation in cold collisions of ¹Σ⁺ molecules with structureless atoms in an external magnetic field. To this end, we develop a rigorous coupled-channel methodology, which accounts for rotational and nuclear spin degrees of freedom of ¹Σ⁺ molecules and their interaction with an external magnetic field as well as anisotropic atom-molecule interactions. We apply the methodology to study the collisional relaxation of the nuclear spin sublevels of ¹³CO molecules immersed in a cold buffer gas of ⁴He atoms. We find that nuclear spin relaxation in the ground rotational manifold (N = 0) of ¹³CO occurs extremely slowly due to the absence of direct couplings between the nuclear spin sublevels. The rates of collisional transitions between the rotationally excited (N = 1) nuclear spin states of ¹³CO are generally much higher due to the direct nuclear spin-rotation coupling between the states. These transitions obey selection rules, which depend on the values of space-fixed projections of rotational and nuclear spin angular momenta (M and M) for the initial and final molecular states. For some initial states, we also observe a strong magnetic field dependence, which can be understood by using the first Born approximation. We use our calculated nuclear spin relaxation rates to investigate the thermalization of a single nuclear spin state of ¹³CO(N = 0) immersed in a cold buffer gas of ⁴He. The calculated nuclear spin relaxation times (T₁ ≃ 1 s at T = 1 K at a He density of 10^-14 cm^-3) display a steep temperature dependence decreasing rapidly at elevated temperatures due to the increased population of rotationally excited states, which undergo nuclear spin relaxation at a much faster rate. Thus, long relaxation times of N = 0 nuclear spin states in cold collisions with buffer gas atoms can be maintained only at sufficiently low temperatures (kT ≪ 2B), where B is the rotational constant.