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

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) $1s\sigma -$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.

References in corpus (4)

• Bound state properties and photodetachment of the negatively charged hydrogen ions
• Highly accurate bound state calculations of the two-center molecular ions by using the universal variational expansion for three-body systems
• On the general theory of bound state spectra in the Coulomb few- and many-body systems
• On the interpolation formula for the bound state energies of atomic systems

Cited by in corpus (1)

• Mass-dependencies of the bound state properties for three-body positronium-like exitonic complexes