Electron Correlation in the Ground State of Helium

Formulae are obtained for the distribution function f(r12) of the interelectronic distance r12 in the ground state of helium, and for the mean value of any positive integral power of r12. Five different wave functions are considered, showing varying degrees of electron correlation. The greater the degree of correlation the larger is the mean electronic separation. Curves of f(r12) are plotted, and from them the size and depth of the Coulomb hole are evaluated. There is a close correlation between the mean value of 1/r12 and the error in the energy as calculated with these five wave functions.