Additive and nonadditive potentials in a hybrid system: Ground state atom, excited state atom, and ion

The long-range additive and nonadditive potentials for a three-body hybrid atom-ion system composed of one ground S state Li atom, one excited P state Li atom and one ground S state Li⁺ ion are  studied theoretically. The interaction coefficients are evaluated with highly accurate wave functions calculated variationally in Hylleraas coordinates. We find for this hybrid system in particular geometrical arrangements the two-body additive interactions sum to zero leaving only three-body nonadditive collective interactions. We also present a precise evaluation of the coefficients up to order R^-6 in the long-range potentials for electronic states of Li₂⁺ correlating to Li⁺ (1 S) - Li(2 P).