Correlation energy of two electrons in the high-density limit

Abstract

We consider the high-density-limit correlation energy \Ec in $D \ge 2$ dimensions for the $^1S$ 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 \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 \sim -\delta^2/8 in any confining external potential, where $\delta = 1/(D-1)$.Comment: 4 pages, 0 figur