Nuclear Spin Relaxation in Cold Atom–Molecule Collisions

Abstract

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 N and M I ) 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 (T 1 ≃ 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 (k B T ≪ 2B e ), where B e is the rotational constant.

Cold Chemistry

“…By contrast, Hermsmeier et al consider nuclear spins, taking advantage of ultracold collision energies to explore the detailed arena of spin-changing collisions of 13 CO with helium buffergas atoms. 17 A dramatic difference in these rates between the N = 0 and N = 1 states of the molecules highlights the exquisite sensitivity of cold collision dynamics to details of the hyperfine Hamiltonian. Finally, a longstanding area of interest in ultracold collisions is to probe the forest of Fano-Feshbach resonances that can occur as a magnetic field is varied.…”

“…The differences emerge in a set of striking reversals of excitation selection rules, between H 2 O and D 2 O. By contrast, Hermsmeier et al consider nuclear spins, taking advantage of ultracold collision energies to explore the detailed arena of spin-changing collisions of 13 CO with helium buffer-gas atoms . A dramatic difference in these rates between the N = 0 and N = 1 states of the molecules highlights the exquisite sensitivity of cold collision dynamics to details of the hyperfine Hamiltonian.…”