We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, n electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schrödinger perturbation theory to show that, in the high-density regime, the ground-state reduced (i.e., per electron) energy can be expanded as $\epsilon (r_s,n) = \epsilon _0(n) r_s^{-2} + \epsilon _1(n) r_s^{-1} + \epsilon _2(n) +\epsilon _3(n) r_s\break + \cdots\,$, where rs is the Seitz radius. We use strong-coupling perturbation theory and show that, in the low-density regime, the reduced energy can be expanded as $\epsilon (r_s,n) = \eta _0(n) r_s^{-1} + \eta _1(n) r_s^{-3/2}\break + \eta _2(n) r_s^{-2} + \cdots\,$. We report explicit expressions for ε0(n), ε1(n), ε2(n), ε3(n), η0(n), and η1(n) and derive the thermodynamic (large-n) limits of each of these. Finally, we perform numerical studies of UEGs with n = 2, 3, …, 10, using Hylleraas-type and quantum Monte Carlo methods, and combine these with the perturbative results to obtain a picture of the behavior of the new model over the full range of n and rs values.
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