Thomas-Fermi scaling in the energy spectra of atomic ions
Abstract
The energy spectra of atomic ions are re-examined from the point of view of Thomas-Fermi scaling relations. For the first ionization potential, which sets the energy scale for the true discrete spectrum, Thomas-Fermi theory predicts the following relation: Eioniz=Z2 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. We provide an analytic expression for g, with two adjustable parameters, 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 with a single exponential: Nstates=exp (Delta E/Theta), where Delta E is the excitation energy, leads to a parameter, Theta, exhibiting a universal scaling a la Thomas-Fermi: Theta=Z2 N-4/3 h(N/Z), where h is approximately linear near N/Z=1.