Random phase approximation

The random phase approximation treats the independent-particle response to the self-consistent total field, including the induced mean Coulomb potential. With a positive static number-response coefficient ${\Pi }_0=-\delta n/\delta U$, a potential $U=-e\varphi$ gives $\delta n=e{\Pi }_0{\varphi }_{\mathrm{tot}}$. Combining induced charge $-e\delta n$ with Poisson equation gives $ϵ=1+e^2{\Pi }_0/({ϵ}_0{q}^2)$. Exchange-correlation vertex corrections beyond this self-consistent response are omitted. It is a response approximation, not a literal assumption that every microscopic electron phase is independently randomized.