Accurate mass-interpolation and mass-asymptotic formulas are derived for one- and two-center three-body ions with unit charges. The derived formulas are applied to predict accurate numerical values of the total energies of the ground (bound) $1^{ 1}S(L = 0)-$states in one-center atomic ions $X^{ +} e^{ -} e^{ -}$ and analogous ground (bound) $1 s \sigma-$states in the two-center, quasi-adiabatic (or quasi-molecular) $X^{ +} X^{ +} e^{ -}$ ions. We also discuss a few problems which currently remain unsolved for the $Q^{ -1}$ expansions constructed for the ground (bound) states in few-electron atoms and ions.
Categories: physics.atom-ph