Novel adiabatic invariant for the three-body Coulomb problem

Journal Article · Fri Sep 22 04:00:00 EDT 1995 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.470585· OSTI ID:251126

Mueller, J ^[1]; Burgdoerfer, J ^[1]; Noid, D W ^[2]

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1. Department of Physics, University of Tennessee, Knoxville, Tennessee 37996-1200 (United States)
2. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6377 (United States)

The two-(fixed) center Coulomb problem possesses in nonrelativistic mechanics, besides the ``classical`` constants of motion, an additional constant of motion associated with dynamical symmetry and separability of the problem. When the motion of the nuclei is taken into account the constant of motion is destroyed but reappears as an adiabatic invariant. We have identified this novel adiabatic invariant for the unrestricted three-body problem in the limit of two heavy particles and one light particle. Unlike all other known adiabatic invariants, it is globally conserved to order {delta}={ital m}/{ital M} in the light- to heavy-mass ratio. The significance of this invariant for the semiclassical description of the chemical bond and for diatomic molecules beyond the Born--Oppenheimer approximation is discussed. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

• Research Organization: Oak Ridge National Laboratory
• DOE Contract Number: AC05-84OR21400; FG05-87ER40361
• OSTI ID: 251126
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 12 Vol. 103; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ADIABATIC INVARIANCE
BORN-OPPENHEIMER APPROXIMATION
CHEMICAL BONDS
COULOMB FIELD
ELECTRON CORRELATION
ELECTRONIC STRUCTURE
HAMILTONIAN FUNCTION
IONS
QUANTUM MECHANICS
THREE-BODY PROBLEM
TRAJECTORIES