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We consider the long-range states expected for complexes formed from analkali-metal diatomic molecule in a singlet state and an alkali-metal atom. Weexplore the structure of the Hamiltonian for such systems, and the couplingsbetween the six angular momenta that are present. We consider the patterns anddensities of the long-range states, and the terms in the Hamiltonian that cancause Feshbach resonances when the states cross threshold as a function ofmagnetic field. We present a case study of $^{40}$K$^{87}$Rb+$^{87}$Rb. We showmultiple types of resonance due to long-range states with rotational and/orhyperfine excitation, and consider the likelihood of them existing at low tomoderate magnetic fields.

Long-range states and Feshbach resonances in collisions between ultracold alkali-metal diatomic molecules and atoms