We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge Z > 0 and N quantum electrons of charge -1 is E(N,Z) = -1/2Z ~2lnZ + (E ~(TF)(λ) + 1/2c ~H)Z ~2 + o(Z ~2) when Z → ∞ and N/Z → λ, where E ~(TF)(λ) is given by a Thomas-Fermi type variational problem and c H ≈ -2.2339 is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when Z → ∞, which is contrary to the expected behavior of three-dimensional atoms.
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