Abstract
Witten's generalization to arbitrary dimension has afforded new insight into the correlated motion of quantum particles [Phys. Today 33, (7), 38 (1980)]. We have used a classically based method to understand the resultant dimensionality dependence of the ground-state energy of the helium atom in the approximation which regards the quantum fluctuations of the system as being harmonic oscillations about a classical, correlated state of minimum effective potential energy. Making an analogy with thermal systems, this provides a phase diagram'' of a single helium atom that features a first-order melting transition, with inverse dimensionality playing the role of temperature. Our approximation gives an understanding of the high-dimensionality behavior of the quantum solution found with a perturbation theory expansion in inverse dimensionality by Goodson and Herschbach [Phys. Rev. Lett. 58, 1628 (1987)]. From comparison with variational quantum ground-state solutions by Loeser and Herschbach [J. Chem. Phys. 84, 3882 (1986)] for atomic numbers 2, 3, and 6 we find that the harmonic description improves with decreasing nuclear charge.
Published Version
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