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It is shown that the ground state energy of heavy atoms is, to leading order,given by the non-relativistic Thomas-Fermi energy. The proof is based on therelativistic Hamiltonian of Brown and Ravenhall which is derived from quantumelectrodynamics yielding energy levels correctly up to order $\alpha^2$Ry

The ground-state energy of heavy atoms according to Brown and Ravenhall: absence of relativistic effects in leading order