Long-range additive and nonadditive potentials in a hybrid system: Ground-state atom, excited-state atom, and ion

We report a theoretical study on the long-range additive and nonadditive potentials for a three-body hybrid atom-atom-ion system composed of one ground-S -state Li atom, one excited-P -state Li atom, and one ground-S -state Li⁺ ion, Li (2 ²S ) -Li (2 ²P ) -Li⁺(1 ¹S ). The interaction coefficients are evaluated with highly accurate wave functions calculated variationally in Hylleraas coordinates. For this hybrid system the three-body nonadditive interactions (appearing in second order) induced by the energy degeneracy and enhanced by the induction effect of the Li⁺ ion through the internal electric field can be strong and even stronger than the two-body additive interactions at the same order. We find that for particular geometries the two-body additive interactions of the system sum to zero, leaving only three-body nonadditive interactions, thus making the present system potentially a platform to explore quantum three-body effects. We also extract by first principles the leading coefficients of the long-range electrostatic, induction, and dispersion energies of Li₂⁺ electronic states correlating to Li+(1^{1S ) -Li(2 2P ) . The results should be especially valuable for the exploration of schemes to create trimers with ultracold atoms and ions in optical lattices.}