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The energy spectra of atomic ions are re-examined from the point of view ofThomas-Fermi scaling relations. For the first ionization potential, which setsthe energy scale for the true discrete spectrum, Thomas-Fermi theory predictsthe following relation: E_{ioniz}=Z^2 N^{-2/3} g(N/Z), where Z is the nuclearcharge, N is the number of electrons, and g is a function of N/Z. This relationdoes not hold for neutral atoms, but works extremely well in the cationicdomain, Z>N. We provide an analytic expression for g, with two adjustableparameters, which fits the available experimental data for more than 380 ions.In addition, we show that a rough fit to the integrated density of states witha single exponential: N_{states}=exp (Delta E/Theta), where Delta E is theexcitation energy, leads to a parameter, Theta, exhibiting a universal scalinga la Thomas-Fermi: Theta=Z^2 N^{-4/3} h(N/Z), where h is approximately linearnear N/Z=1.

Thomas-Fermi scaling in the energy spectra of atomic ions