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Second-order energies and limiting correlation energies in two-electron systems.
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We consider the high-density-limit correlation energy in dimensions for the ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the values are strikingly similar, depending strongly on but only weakly on the external potential. We conjecture that for large , the limiting correlation energy in any confining external potential, where .
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