Highly accurate bound state calculations of the two-center molecular ions by using the universal variational expansion for three-body systems

TL;DR

This paper introduces a universal variational expansion method for highly accurate bound state calculations in three-body systems, especially focusing on hydrogen molecular ions with various isotopes and heavy nuclei.

Contribution

The paper develops and applies a universal variational expansion technique for precise numerical computation of bound states in arbitrary three-body Coulomb systems, including those with heavy nuclei.

Findings

Achieved highly accurate bound state spectra calculations for hydrogen molecular ions.

Demonstrated the method's applicability to systems with arbitrary particle masses and charges.

Provided results for systems with both finite and infinite nuclear masses.

Abstract

The universal variational expansion for the non-relativistic three-body systems is explicitly constructed. Three-body universal expansion can be used to perform highly accurate numerical computations of the bound state spectra in arbitrary three-body systems, including Coulomb three-body systems with arbitrary particle masses and electric charges. Our main interest is related to the adiabatic three-body systems which contain one bound electron and two heavy nuclei of hydrogen isotopes: the protium $p$, deuterium $d$ and tritium $t$. We also consider the analogous (model) hydrogen ion ${}^{\infty}$H$^{+}_2$ with the two infinitely heavy nuclei. PACS number(s): 36.10.-k and 36.10.Dr