Thomas-Fermi scaling in the energy spectra of atomic ions

TL;DR

This paper investigates Thomas-Fermi scaling laws in atomic ion energy spectra, deriving relations for ionization potential and density of states that align well with experimental data for ions, revealing universal scaling behaviors.

Contribution

It introduces a new scaling relation for ionization potential and density of states in atomic ions, supported by analytic expressions and experimental data fitting.

Findings

Thomas-Fermi scaling accurately describes ionization potentials of ions.

Derived analytic expression for the scaling function g(N/Z).

Universal scaling law for the temperature parameter Theta.

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: 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. 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: N_{states}=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=Z^2 N^{-4/3} h(N/Z), where h is approximately linear near N/Z=1.