Spin-resolved pair-distribution functions in an electron gas: A scattering approach based on consistent potentials

The spin-resolved pair-functions $g_{\uparrow \downarrow }\left(r\right)$ and $g_{\uparrow \uparrow }\left(r\right)$ of an interacting unpolarized electron gas are calculated. The calculations are based on geminal representations of two-electron states and physically motivated model potentials, $V_{\uparrow \downarrow }\left(r\right)$ and $V_{\uparrow \uparrow }\left(r\right)$, in the scattering Schrödinger equations for relative movements. The proper normalization conditions for the pair functions, as natural constraints, are used to obtain consistent effective potentials. Good agreement with data of quantum Monte Carlo treatment on the pair-distribution functions is established. Possible applications of the potentials in other two- and one-particle characteristics are briefly discussed.

Figure 1

Numerically determined consistent screening parameters to Eqs. (9, 10), as a function of the Fermi momentum (density parameter). The dashed-dotted lines are based on linear fitting, see Eqs. (12, 13).

Figure 2

The $r_{s}g(r=0)$ function as a function of the density parameter $r_s$. The solid curve (solid squares) is the present result. The dashed-dotted curve refers to the analytic expression of Overhauser. The dotted and dashed curves are based on the exact high-density expression and ladder approximation, respectively. Solid triangles are the results of numerical solution of an effective Euler-Lagrange equation.

Figure 3

Pair-correlation functions at $r_s=1$, as a function of the $(r∕r_s)$-variable. Solid squares, up triangles, and down triangles refer to Monte Carlo data.

Figure 4

The same as in Fig. 3, at the $r_s=5$ density parameter.