Conductivity of a metal with inverse-power-law correlated impurities

We calculate the cooperon for a system of noninteracting electrons in the presence of random potentials with correlations W(r)=${\mathit{W}}_0$δ(r)+${\mathit{W}}_1$${\mathit{r}}^{\mathrm{-}(\mathit{d}+\mathrm{\sigma })}$ in d dimensions, for arbitrary values σ and d, to first order in ${\mathit{W}}_1$. Our detailed results confirm the exactitude of the universal form for the cooperon proposed earlier by other authors based on general principles. We find that the system will have short-range (long-range) behavior according to σ being positive (negative).