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-up arrowdown arrow(r)=V-down arrowup arrow(r). The simple original Overhauser model interaction, independent of the relative spin polarization zeta, does not capture the zeta dependence of the correlation contribution to g(r=0).