On highly accurate, bound state calculations of the molecular diatomic ions

Abstract

Results of highly accurate calculations obtained recently for a number of Coulomb two-centre ions with the unit electrical charges and are presented. In particular, we have determined (to very high accuracy) the total energies and other bound state properties of the ground (bound) states in the two-centre adiabatic (or molecular) H, D, HD, HT, T and DT ions. In these computations we used the new masses of hydrogen isotopes, which have been measured in recent high-energy experiments. Theory of soft adiabatic three-body systems with the unit electrical charges is also discussed. An accurate mass-interpolation formula is derived and tested for the total energies of model two-centre ions with very heavy masses of the point particles ( 100,000 ). This formula allows one to evaluate (to high accuracy) the total energies and other bound state properties of arbitrary two-centre ions, including very heavy systems. We also determine the upper mass limit for applicability of our universal expansion in the relative and/or perimetric coordinates. Highlights An effective procedure is developed for highly accurate numerical computations of bound states in the two-center molecular ions. Properties of many actual two-center ions, including the both and ions, have been determined to very high accuracy. Theory of the soft adiabatic (two-center) three-body systems is developed. Properties of these ions are now known to high accuracy. Accurate numerical method which allows one to predict the total energies and other properties of truly adiabatic systems with very large (or infinite) nuclear masses has been proposed, applied and studied in detail.