Correlation energy of two electrons in a ball

We study the ground-state correlation energy E(c) of two electrons of opposite spin confined within a D-dimensional ball (D > or = 2) of radius R. In the high-density regime, we report accurate results for the exact and restricted Hartree-Fock energy, using a Hylleraas-type expansion for the former and a simple polynomial basis set for the latter. By investigating the exact limiting correlation energy E(c)(0) = lim(R-->0)E(c) for various values of D, we test our recent conjecture [P.-F. Loos and P. M. W. Gill, J. Chem. Phys. 131, 241101 (2009)] that in the large-D limit, E(c)(0) approximately -delta(2)/8 for any spherically symmetric confining external potential, where delta = 1/(D-1).