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We investigate theoretically the long-range electrostatic interactionsbetween a ground-state homonuclear alkali-metal dimer and an excitedalkali-metal atom taking into account its fine-structure. The interactioninvolves the combination of first-order quadrupole-quadrupole and second-orderdipole-dipole effects. Depending on the considered species, the atomicspin-orbit may be comparable to the atom-molecule electrostatic energy and tothe dimer rotational structure. Here we extend our general description in theframework of the second-order degenerate perturbation theory [M. Lepers and O.Dulieu, Eur. Phys. J. D, 2011] to various regimes induced by the magnitude ofthe atomic spin-orbit. A complex dynamics of the atom-molecule may take placeat large distances, which may have consequences for the search for an universalmodel of ultracold inelastic collisions as proposed for instance in [Z.Idziaszek and P. S. Julienne, Phys. Rev. Lett. \textbf{104}, 113202 (2010)].

Long-range interactions between ultracold atoms and molecules including atomic spin-orbit