Abstract
We present an analytical expression for the static many-body local field factor ${G}_{+}(q)$ of a homogeneous two-dimensional electron gas, which reproduces diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number q. This allows us to also provide a closed-form expression for the exchange and correlation kernel ${K}_{\mathrm{xc}}(r),$ which represents a key input for density functional studies of inhomogeneous systems.
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