Correlation energy of two electrons in the high-density limit

摘要

We consider the high-density-limit correlation energy E_c in D≥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 E_c～-δ~2 /8 in any confining external potential, where δ =1/ (D-1).