Calculation of pair correlations in a high-density electron gas: Constraints for effective interparticle potentials

The pair-correlation function g(r) of an interacting, unpolarized electron gas is modelled by using the geminal representation and effective potentials for the two-electron relative motion. We put forward a generalization of the impurity-related Fumi theorem, in order to obtain the scattering-mediated part of the kinetic energy change. Considering the high-density limit, where a perturbatively exact expression for the ground-state energy is available, a rigorous constraint on the effective interactions in the even and odd channels is deduced. The constraint is implemented by using physically motivated one-parametric potentials in these channels.