Invariance of the correlation energy at high density and large dimension in two-electron systems

Abstract

We prove that, in the large-dimension limit, the high-density correlation energy $\Ec$ of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by $\Ec \sim -1/(8D^2)$ for any radial confining potential $V(r)$. This result explains the observed similarity of $\Ec$ in a variety of two-electron systems in three-dimensional space.

4 pages, 1 figure, to appear in Phys. Rev. Lett

References in corpus (4)

• Two electrons on a hypersphere: a quasi-exactly solvable model
• Ground state of two electrons on a sphere
• Correlation energy of two electrons in the high-density limit
• Correlation energy of two electrons in a ball

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