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We consider the magnetically tunable Feshbach resonances that may exist inultracold mixtures of molecules in $^2\Sigma$ states and alkali-metal atoms. Wefocus on Rb+CaF as a prototype system. There are likely to be Feshbachresonances analogous to those between pairs of alkali-metal atoms. Weinvestigate the patterns of near-threshold states and the resonances that theycause, using coupled-channel calculations of the bound states and low-energyscattering on model interaction potentials. We explore the dependence of theproperties on as-yet-unknown potential parameters. There is a high probabilitythat resonances will exist at magnetic fields below 1000 G, and that these willbe broad enough to control collisions and form triatomic molecules bymagnetoassociation. We consider the effect of CaF rotation and potentialanisotropy, and conclude that they may produce additional resonances but shouldnot affect the existence of rotation-free resonances.

Tunable Feshbach resonances in collisions of ultracold molecules in $^2\Sigma$ states with alkali-metal atoms