We evaluate the leading-order corrections (in $r_s)$ to the static polarization ${\mathrm{\Pi }}^{\mathrm{*}}$ $\mathrm{}(q,0\mathrm{}),$ of the two-dimensional electron gas with dynamically screened interactions. The corresponding diagrams all exhibit singular logarithmic behavior in their derivatives about ${q=2k}_F$ and provide significant enhancement of the proper polarization particularly at low densities. At a density of $r_s=3,$ the contribution from the leading-order fluctuational diagrams exceeds both the zeroth-order (Lindhard) response and the self-energy and exchange contributions. The importance of these diagrams in two-dimensions is demonstrated by comparison to those of an equivalent three-dimensional electron gas; we also consider the impact these findings have on ${\mathrm{\Pi }}^{\mathrm{*}}$ $\mathrm{}(q,0\mathrm{})\mathrm{}$ computed to all orders in perturbation theory.

• Received 16 November 2001

DOI:https://doi.org/10.1103/PhysRevB.65.195309