Inclusion of the discreteness of the electronic spectrum in the statistical model of free ions

The characteristics of free positive ions have been studied with a semiclassical method based on the Thomas-Fermi statistical model. An efficient method has been proposed for the inclusion of the discreteness of the electronic spectrum and the calculation of a shell correction to the number of states by the statistical model in the case of the strong irregularity of the correction. The calculation of the free-ion ionization potentials within this approach reproduces the “sawtooth” dependence of these potentials on the ion charge and strongly improves the description of the experimental data by the statistical model.