Abstract
Supermultiplet patterns indicating pronounced collective motion of electrons are prominent among intrashell excited states of helium or alkaline earth atoms. Many aspects of these patterns have previously been discussed in terms of an empirical rovibrator model, e-core-e, analogous to alinear triatomic molecule. However, this has appeared incompatible with a dimensional scaling treatment that predicts pseudomolecular features and relates properties of some excited states to the ground state, but corresponds to abent equilibrium geometry. We examine both the full two-electron Hamiltonian, including angular momentum, and a prototype model for angular correlation which restricts the two particles to the surface of a sphere. By virtue of the boundary conditions imposed by the Jacobian volume element, we find that alinear equilibrium geometry is not allowed. If the Hamiltonian is transformed to reduce the Jacobian to unity, an infinite barrier appears in the effective potential when the electrons are 180° apart and equidistant from the nucleus. We find the supermultiplet patterns, including some “antimolecular” features, are consistent with a floppy butbent geometry, anasymmetric rotor model. The most probable interelectron angle ϑ m varies markedly with the principal quantum number and also with the space-quantization of the angular momentum with respect to body-fixed axes.
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Herschbach, D.R., Loeser, J.G. & Watson, D.K. Pseudomolecular atoms: geometry of two-electron intrashell excited states. Z Phys D - Atoms, Molecules and Clusters 10, 195–210 (1988). https://doi.org/10.1007/BF01384854
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DOI: https://doi.org/10.1007/BF01384854