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| Paper IPM / Physic / 6875 |
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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. 73, 683 (1995)] and further evaluated by P. Gori-Giorgi and J. P. Perdew [Phys. Rev. B 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.
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