The Jastrow-Feenberg functional variation method is applied to study electron correlations in atomic systems. The density and pair distributions of electrons are calculated by solving Euler-Lagrange equations for the pair distribution functions. From the calculated pair distributions, we examine the local structure of the exchange-correlation holes and find a sensitive dependence on the location of the electrons. Our theory gives correlation energies in good agreement with experimental data. We compare our results wit those from density functional theories.