Faddeev-Born-Oppenheimer equations for molecular three-body systems: Application to H/sub 2/ /sup +/
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), Vol. 36:10
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
HYDROGEN IONS
ELECTRONIC STRUCTURE
THREE-BODY PROBLEM
COULOMB FIELD
DIAGRAMS
EIGENFUNCTIONS
ENERGY LEVELS
FADDEEV EQUATIONS
MOLECULES
PARTICLE INTERACTIONS
POTENTIAL ENERGY
CHARGED PARTICLES
ELECTRIC FIELDS
ENERGY
EQUATIONS
FUNCTIONS
INTERACTIONS
IONS
MANY-BODY PROBLEM
640302* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory