# Asymptotic and interpolation series for the Coulomb three-body systems with unit charges

## TL;DR

This paper develops accurate formulas for predicting the energies of three-body Coulomb systems with unit charges, aiding in understanding atomic and molecular ion states.

## Contribution

It introduces new mass-interpolation and asymptotic formulas for three-body ions, improving energy predictions for one- and two-center systems with unit charges.

## Key findings

- Derived formulas accurately predict ground state energies.
- Applied formulas to specific atomic and molecular ions.
- Discussed unresolved problems in Q^{-1} expansions for few-electron systems.

## Abstract

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.