Correlation energy of two electrons in the high-density limit

We consider the high-density-limit correlation energy Ec in D≥2 dimensions for the ¹Sground 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 Ec values are strikingly similar, depending strongly on D but only weakly on the external potential. We conjecture that for large D, the limiting correlation energy Ec∼−δ2/8 in any confining external potential, where δ=1/(D−1).P.M.W.G. thanks the APAC Merit Allocation Scheme for a grant of supercomputer time, and the Australian Research Council Grant Nos. DP0664466 and DP0771978 for funding