On bound state spectra of the one-electron diatomic ions

TL;DR

This paper computes high-accuracy total energies for various one-electron diatomic ions and derives interpolation formulas applicable to symmetric and non-symmetric cases, addressing unresolved problems in the field.

Contribution

It provides precise numerical energies and new mass-interpolation formulas for one-electron diatomic ions, enhancing understanding of their bound state spectra.

Findings

High-accuracy total energies for diatomic ions calculated.

Derived mass-interpolation formulas for symmetric and non-symmetric ions.

Addressed unresolved problems in two-center one-electron ions.

Abstract

The total energies of a large number of diatomic (or two-center) one-electron $A^{+} B^{+} e^{-}$ ions with unit electrical charges are determined numerically to high accuracy. Based on these results we derive some accurate mass-interpolation formulas for the total energies of such three-body systems (ions). These formulas can be applied to the both symmetric $A^{+} A^{+} e^{-}$ and non-symmetric $A^{+} B^{+} e^{-}$ diatomic ions. Based on the results obtained in this study we also consider a few actual and currently unsolved problems, which are known for the two-center (or diatomic) one-electron ions.