Self-consistent Overhauser model for the pair distribution function of   an electron gas at finite temperature
  We present calculations of the spin-averaged pair distribution function $g(r)$ in a homogeneous gas of electrons moving in dimensionality D=3 or D=2 at finite temperature. The model involves the solution of a two-electron scattering problem via an effective potential which embodies many-body effects through a self-consistent Hartree approximation, leading to two-body wave functions to be averaged over a temperature-dependent distribution of relative momentum for electron pairs. We report illustrative numerical results for $g(r)$ in an intermediate-coupling regime and interpret them in terms of changes of short-range order with increasing temperature. 
R. Asgari, M. Cardenas, M. Polini, B. Davoudi and M. P. Tosi