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 A. W. Overhauser [Can. J. Phys. {\bf 73}, 683
(1995)] and further evaluated by P. Gori-Giorgi and J. P. Perdew [Phys. Rev. B
{\bf 64}, 155102 (2001)]. The model involves the solution of a two-electron
scattering problem via an effective Coulombic potential, that 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 rs, extending up to rs≈10 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 rs=5 in D=2, and has limited accuracy in regard to the spin-resolved
components g↑↑(r) and g↑↓(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.Comment: 14 pages, 7 figuers, to apear in Physical Review