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Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $ρ$ and a new two-electron parameter $η$. We outline a systematic strategy to determine a new density functional $E(ρ,η)$ across the spectrum of possible $ρ$ and $η$ values.