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We consider an atom described by M\"uller theory, which is similar toHartree-Fock theory, but with a modified exchange term. We prove that a nucleusof charge Z can bind at most Z+C electrons, where C is a universal constant.Our proof proceeds by comparison with Thomas-Fermi theory and a key ingredientis a novel bound on the number of electrons far from the nucleus.

The maximal excess charge in M\"uller density-matrix-functional theory