  We consider the magnetically tunable Feshbach resonances that may exist in
ultracold mixtures of molecules in $^2\Sigma$ states and alkali-metal atoms. We
focus on Rb+CaF as a prototype system. There are likely to be Feshbach
resonances analogous to those between pairs of alkali-metal atoms. We
investigate the patterns of near-threshold states and the resonances that they
cause, using coupled-channel calculations of the bound states and low-energy
scattering on model interaction potentials. We explore the dependence of the
properties on as-yet-unknown potential parameters. There is a high probability
that resonances will exist at magnetic fields below 1000 G, and that these will
be broad enough to control collisions and form triatomic molecules by
magnetoassociation. We consider the effect of CaF rotation and potential
anisotropy, and conclude that they may produce additional resonances but should
not affect the existence of rotation-free resonances.
