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For the first ionization potential, which sets the energy scale for the true discrete spectrum, Thomas-Fermi theory predicts the following relation: E_{ioniz}=Z^2 N^{-2/3} g(N/Z), where Z is the nuclear charge, N is the number of electrons, and g is a function of N/Z. This relation does not hold for neutral atoms, but works extremely well in the cationic domain, Z>N. 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