Mean total and orbital excitation energies of atomic ions in two approaches of the Thomas–Fermi theory

Abstract

The mean excitation energy is a nontrivial material property that depends on the excitation spectra of atoms and molecules. It is a crucial input for the evaluation of the energy deposition of swift charged particles. In Bethe's theory of the stopping cross section, it is determined from the dipole oscillator strength, while in the Lindhard and Scharff theory, it is given in terms of the material response through the Local Plasma Approximation. This work is dedicated to Jack Sabin's motto: a simple model is worth exploring before a sophisticated theory. Following this idea, here we regain old theories such as the Thomas–Fermi model and the original Local Plasma Approximation to study the mean excitation energy of neutral atoms and their cations. We implement two approaches, the Thomas–Fermi theory with Amaldi corrections for ionic systems and complement our work with a more sophisticated DFT-like Thomas–Fermi–Dirac–Weizsäcker approximation. Using the obtained total mean excitation energies for C, F, Ne, Si, Cl, Sc, Mn, and Zn and their cations, the single-electron mean excitation energy is determined allowing for a reasonable description of orbital and shell contributions as compared with more sophisticated theories.