Nuclear Spin Relaxation in Cold Atom-Molecule Collisions

We explore the quantum dynamics of nuclear spin relaxationin coldcollisions of (1)& sigma;(+) molecules with structurelessatoms in an external magnetic field. To this end, we develop a rigorouscoupled-channel methodology, which accounts for rotational and nuclearspin degrees of freedom of (1)& sigma;(+) moleculesand their interaction with an external magnetic field as well as anisotropicatom-molecule interactions. We apply the methodology to studythe collisional relaxation of the nuclear spin sublevels of (CO)-C-13 molecules immersed in a cold buffer gas of He-4 atoms.We find that nuclear spin relaxation in the ground rotational manifold(N = 0) of (CO)-C-13 occurs extremely slowlydue 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 (CO)-C-13 aregenerally much higher due to the direct nuclear spin-rotationcoupling between the states. These transitions obey selection rules,which depend on the values of space-fixed projections of rotationaland nuclear spin angular momenta (M ( N ) and M ( I )) for theinitial and final molecular states. For some initial states, we alsoobserve a strong magnetic field dependence, which can be understoodby using the first Born approximation. We use our calculated nuclearspin relaxation rates to investigate the thermalization of a singlenuclear spin state of (CO)-C-13-(N = 0) immersedin a cold buffer gas of He-4. The calculated nuclear spinrelaxation times (T (1) & SIME; 1 s at T = 1 K at a He density of 10(-14) cm(-3)) display a steep temperature dependence decreasingrapidly at elevated temperatures due to the increased population ofrotationally excited states, which undergo nuclear spin relaxationat a much faster rate. Thus, long relaxation times of N = 0 nuclear spin states in cold collisions with buffer gas atomscan be maintained only at sufficiently low temperatures (k ( B ) T MUCH LESS-THAN 2B ( e )), where B ( e ) is the rotational constant.