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- W1985071579 abstract "We consider the correlation of two particles on a sphere interacting via various repulsive forces: a Coulomb repulsion, a Gaussian, and a $ensuremath{delta}$ function. This rigid-bender picture with Coulomb repulsion provides a schematic model of intrashell angular correlation in doubly excited two-electron atoms. We examine energy levels and reduced densities $ensuremath{rho}({ensuremath{theta}}_{12})$ for states corresponding to shells ${n}_{1}={n}_{2}=2,3,4$. Energy levels for fully converged states fall into remarkable rovibrator patterns, as found in the corresponding three-dimensional case by Kellman and Herrick. The rovibrator nature of the states is directly reflected in plots of $ensuremath{rho}({ensuremath{theta}}_{12})$, which reveal both collective rotations and vibrations and even the influence of centrifugal distortion. A minimal basis (${l}_{max}=nensuremath{-}1$) is inadequate to represent angular correlation in the higher-energy states of each shell. The repulsive Gaussian potential, which is finite at ${ensuremath{theta}}_{12}=0$, shows the onset of independent-particle shell-model behavior in higher-energy states. Comparison of the Coulomb case with the delta-function potential exhibits the degree to which kinematics governs wave-function character." @default.
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- W1985071579 date "1982-03-01" @default.
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- W1985071579 title "Correlation of two particles on a sphere" @default.
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- W1985071579 doi "https://doi.org/10.1103/physreva.25.1513" @default.
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