Simple physical picture of the Overhauser screened electron-electron interaction

As shown by Overhauser and others, the pair-distribution function $g(r)$ of a many-electron system may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion $V(r).$ We propose a simple physical picture in which this screened repulsion is the ``dressed-dressed'' interaction between two neutral objects, each an electron surrounded by its full-coupling exchange-correlation hole. For the effective interaction between two electrons of antiparallel spin in a high-density uniform electron gas of arbitrary spin polarization, we confirm that this picture is qualitatively correct. In contrast, the ``bare-dressed'' interaction is too repulsive, and does not have the expected symmetry ${V}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}{(r)=V}_{\ensuremath{\downarrow}\ensuremath{\uparrow}}(r).$ The simple original Overhauser model interaction, independent of the relative spin polarization $\ensuremath{\zeta},$ does not capture the $\ensuremath{\zeta}$ dependence of the correlation contribution to $g(r=0).$