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

We theoretically investigate long-range interactions for a three-body system involving a ground state Li atom, an excited P state Li atom and a ground state Li ion, denoted by Li($2\,^{2}S$)-Li($2\,^{2}P$)-Li$^+$($1\,^{1}S$), with highly accurate variationally-generated nonrelativistic wave functions in Hylleraas coordinates. Using degenerate perturbation theory for the energies up to second-order, we evaluate the coefficients $C_3$ of the first-order induced and dipolar interactions, the coefficients $C_4$, $C_6$ and $C_8$ of the second-order additive interactions and the coefficients $C_5$ and $C_7$ of the second-order nonadditive interactions. Specific values of these coefficients will be given for different configurations of the three nuclei. The calculations are given for three like-nuclei for the cases of hypothetical infinite mass Li nuclei, and of real finite mass $^6{}$Li or $^7{}$Li nuclei. The results may be useful in the study of ultra-cold plasma.