Short-range correlation in an electron gas: A scattering approach

The pair-correlation function at zero interparticle separation $g\left(0\right)\mathrm{}$ of an interacting electron gas is derived by an averaging procedure using the exact enhancement factor for scattered waves of electrons in a model potential. The range of the screened potential is fixed by a physically motivated constraint. Agreement with the result of a many-body method based on summation of ladder diagrams for electron-electron interactions is established. Possible applications of the potential are discussed as well. A nontrivial density-scaling in the thermal resistivity of metals is predicted.