Faddeev-Born-Oppenheimer Equations for Molecular Three-Body Systems: Application to H ⁺₂

Abstract

A non variational molecular like approach is developed for the three-body problem based on the Faddeev equations. Considering a system of two identical heavy particles (atomic nuclei) and a light one (electron) we study the adiabatic limit of the corresponding Faddeev equation in the absence of interaction between the heavy particles and using general heavy-light potentials that are represented in a separable form through Sturmian functions. The resulting rotationally invariant Faddeev two-center eigenfunctions are used to formulate an ansatz for the solution of the full Hamiltonian where all three particles interact. A set of coupled differential Born-Oppenheimer like equations is obtained for the movement of the heavy particles. Numerical calculations are shown for the 1sσg, 2sσg, 3dσg and 2pσu electronic states in ⁺₂ . The resulting molecular energy curves converge to the exact ones when up to thirty six terms are used in the Hilbert-Schmidt expansion of the Coulomb potential. The non-crossing rule for 2sσg and 3dσg curves is verified.