Calculations of long-range three-body interactions for Li($2S$)-Li($2S$)-Li$^{+}$($1S$)

We theoretically investigate long-range interactions between a ground state Li$^+$ ion and two ground state neutral Li atoms with highly accurate variationally-generated wave functions in Hylleraas coordinates. Using perturbation theory for the energies up to third-order, we evaluate the coefficients $C_4$, $C_6$ and $C_8$ of the second order dispersion interactions and the coefficients $C_7$ and $C_9$ of the third-order additive and nonadditive interactions. The nonadditive interactions coefficients depend on the geometrical configurations of this three-body system and on the different positions of the ion for each configuration. Our calculations may be of interest for the study of three-body recombination and for constructing potential energy surfaces.