The function $u\left(i,j\right)=u\left(\left|{\mathbf{r}}_i-{\mathbf{r}}_j\right|\right)$, in terms of which variational trial functions of the Slater-Jastrow type are expressed, is generalized to include dependence on the electron momenta as well as on the electron-pair separations. The resulting Euler equations are used to evaluate the ground-state coulomb correlation energy giving ${ϵ}_c=0.0622\text{log}\left(r_s\right)-0.1441\text{Ry}$, where $r_s$ is the ratio of the radius of a sphere, containing, on average one electron, to the Bohr radius. This correlation energy is 0.050 Ry lower than the corresponding result ${ϵ}_c=0.0622\text{log}\left(r_s\right)-0.094\text{Ry}$ found by Gell-Mann and Brueckner. Also evaluated are the corresponding correlation corrections to the Hartree-Fock (HF) exchange potential energy and to the average exchange charge density as a function of distance. The correction to the HF exchange potential energy is shown to cancel the divergence of the HF exchange energy at the Fermi energy so that the electron effective mass remains finite.

• Received 25 April 2009

DOI:https://doi.org/10.1103/PhysRevB.80.205102