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 ${}^{1}S$ 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 $\Ec \sim -δ^2/8$ in any confining external potential, where $\delta =1/(D-1)$.

4 pages, 0 figure

References in corpus (2)

• Two electrons on a hypersphere: a quasi-exactly solvable model
• Ground state of two electrons on a sphere

Cited by in corpus (5)

• Excited states of spherium
• Hooke's law correlation in two-electron systems
• A Tale of Two Electrons: Correlation at High Density
• Correlation energy of two electrons in a ball
• Ground state of two electrons on concentric spheres