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

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 via a Coulomb potential is given by Ec∼-1/(8D2) 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.