Faddeev-Born-Oppenheimer equations for molecular three-body systems: Application to H/sub 2/ /sup +/

Journal Article · Sun Nov 15 04:00:00 EST 1987 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.36.4585· OSTI ID:5964061

Fonseca, A C; Pena, M T

A nonvariational parameter-free 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 the Hilbert-Schmidt method. 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 1s(sigma)g, 2s(sigma)g, 3d(sigma)g, 2p(sigma)u, and 2p..pi..u electronic states in H/sub 2/ /sup +/. The resulting molecular energy curves appear to converge to the exact ones when up to fifteen terms are used in the Hilbert-Schmidt expansion of the Coulomb potential. The noncrossing rule for 2s(sigma)g and 3d(sigma)g curves is verified in our work.

• Research Organization: Centro Fsica Nuclear, Avenida Gama Pinto 2, 1699 Lisbon, Portugal
• OSTI ID: 5964061
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 36:10; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
CHARGED PARTICLES
COULOMB FIELD
DIAGRAMS
EIGENFUNCTIONS
ELECTRIC FIELDS
ELECTRONIC STRUCTURE
ENERGY
ENERGY LEVELS
EQUATIONS
FADDEEV EQUATIONS
FUNCTIONS
HYDROGEN IONS
INTERACTIONS
IONS
MANY-BODY PROBLEM
MOLECULES
PARTICLE INTERACTIONS
POTENTIAL ENERGY
THREE-BODY PROBLEM