Self-consistent Overhauser model for the pair distribution function of an electron gas in dimensionalities D=3 and D=2 -: art. no. 075110

We present self-consistent calculations of the spin-averaged pair distribution function g(r) for a homogeneous electron gas in the paramagnetic state in both three and two dimensions, based on an extension of a model that was originally proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] and further evaluated by Gori-Giorgi and Perdew [Phys. Rev. B 64, 155102 (2001)]. The model involves the solution of a two-electron scattering problem via an effective Coulombic potential, which we determine within a self-consistent Hartree approximation. We find numerical results for g(r) that are in excellent agreement with quantum Monte Carlo data at low and intermediate coupling strength r(s), extending up to r(s)approximate to10 in dimensionality D=3. However, the Hartree approximation does not properly account for the emergence of a first-neighbor peak at stronger coupling, such as at r(s)=5 in D=2, and has limited accuracy in regard to the spin-resolved components g(up arrowup arrow)(r) and g(up arrowdown arrow)(r). We also report calculations of the electron-electron s-wave scattering length, to test an analytical expression proposed by Overhauser in D=3 and to present new results in D=2 at moderate coupling strength. Finally, we indicate how this approach can be extended to evaluate the pair distribution functions in inhomogeneous electron systems and hence to obtain improved exchange-correlation energy functionals.