Torus quantization of symmetrically excited helium

Journal Article · Sat Feb 01 04:00:00 EST 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.45.1471· OSTI ID:7205873

Mueller, J ^[1]; Burgdoerfer, J ^[2]; Noid, D ^[3]

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

The recent discovery by Richter and Wintgen (J. Phys. B 23, L197 (1990)) that the classical helium atom is not globally ergodic has stimulated renewed interest in its semiclassical quantization. The Einstein-Brillouin-Keller quantization of Kolmogorov-Arnold-Moser tori around stable periodic orbits becomes locally possible in a selected region of phase space. Using a hyperspherical representation we have found a dynamically confining potential allowing for a stable motion near the Wannier ridge. The resulting semiclassical eigenenergies provide a test for full quantum calculations in the limit of very high quantum numbers. The relations to frequently used group-theoretical classifications for doubly excited states and to the periodic-orbit quantization of the chaotic portion of the phase space are discussed. The extrapolation of the semiclassical quantization to low-lying states give remarkably accurate estimates for the energies of all symmetric {ital L}=0 states of helium.

• DOE Contract Number: AC05-84OR21400; FG05-87ER40361
• OSTI ID: 7205873
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 45:3; ISSN 1050-2947; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

664100* -- Theory of Electronic Structure of Atoms & Molecules-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ANIONS
ATOMS
CHARGED PARTICLES
EIGENVALUES
ELEMENTS
ENERGY LEVELS
EXCITED STATES
FLUIDS
GASES
HELIUM
IONS
NONMETALS
POTENTIALS
QUANTIZATION
QUANTUM NUMBERS
RARE GASES
SEMICLASSICAL APPROXIMATION