Regular Article

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

¹ ITAMP, Harvard-Smithonian Center for Astrophysics, MS 14, 60 Garden Street, Cambridge, MA 02138-1516, USA
² Department of Applied Mathematics University of Western Ontario, London, Ontario N6H 5B7, Canada

^a e-mail: alex1975frol@gmail.com

Received: 16 July 2017
Received in final form: 11 January 2018
Published online: 22 March 2018

Abstract

The universal variational expansion for the non-relativistic three-body systems is explicitly constructed. This universal expansion can be used to perform highly accurate numerical computations of the bound state spectra in various 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 ^∞H₂⁺  with the two infinitely heavy nuclei.