= 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 $U=-e\phi$ gives $\delta n=e\Pi_0\phi_{\rm tot}$. Combining induced charge $-e\delta n$ with <Poisson equation> gives $\epsilon=1+e^2\Pi_0/(\epsilon_0q^2)$. 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.
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