Generalized Slater-Jastrow trial function: Application to the electron gas at high density

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Physics and Astronomy


The function u(i, j) = u(vertical bar r(i)- r(j)vertical bar), 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 epsilon(c)=0.0622 log(r(s))-0.1441 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 epsilon(c) = 0.0622 log(r(s))-0.094 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.

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