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Paper IPM / Physic / 6875  


Abstract:  
We present selfconsistent calculations of the spinaveraged 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. 73, 683 (1995)] and further evaluated by P. GoriGiorgi and J. P. Perdew [Phys. Rev. B 64, 155102 (2001)]. The model involves the solution of a twoelectron scattering problem via an effective Coulombic potential, that we determine within a selfconsistent 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} ≈ 10 in dimensionality D=3. However, the Hartree approximation does not properly account for the emergence of a firstneighbor peak at stronger coupling, such as at r_{s}=5 in D=2, and has limited accuracy in regard to the spinresolved components g_{↑↑}(r) and g_{↑↓}(r). We also report calculations of the electronelectron swave 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 exchangecorrelation energy functionals.
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