Eur. Phys. J. D 12, 449-466 (2000)
https://doi.org/10.1007/s100530070006

Ab initio calculation of the J = 0 and J = 1 states of the H⁺₂, D⁺₂ molecular ions

¹ Laboratoire Kastler Brossel, Université Pierre et Marie Curie et École Normale SupérieureLaboratoire associé au CNRS, UMR 8552, T12, Case 74, 4 place Jussieu, 75252 Paris, France
² Département de physique et modélisation, Université d'Évry Val d'Essonne, boulevard F. Mitterrand, 91025 Évry Cedex, France

Received: 23 February 2000
Revised: 24 May 2000
Published online: 15 December 2000

Abstract

A new, non adiabatic, description of the H⁺₂ molecular ion and its isotopomers is proposed: the molecular system is treated as a three body Coulomb system, in the framework of non relativistic quantum mechanics. The method takes advantage of the dynamical symmetries of the system. It relies on the choice of the perimetric coordinates to describe the system, and of a generalized Hylleraas basis, in which the Hamiltonian exhibits strong coupling rules. The method is described in detail both for S and P states (i.e., states of total angular momentum J = 0 or 1). We calculate the energies of all J = 0 or 1 vibrational levels of the H⁺₂ and D⁺₂ molecular ions with a very high accuracy (typically 10^-14 atomic unit). This a considerable improvement over previous calculations. The dependence of these results on the proton to electron mass ratio is also discussed.