Independent-particle-model potentials for atoms and ions with 36<Z≤54 and a modified Thomas-Fermi atomic energy formula

Using the ab initio energy-minimization procedure of Bass, Green, and Wood, we determine two potential parameters, ξ and η, characterizing the independent-particle-model potential of Green, Sellin, and Zachor (GSZ) for atoms and positive ions with 36<Z≤54. This extends earlier modified-Hartree-Fock (MHF) calculations of Szydlik and Green and of Green, Garvey, and Jackman. We find that both of the parameters in question display, to a good approximation, a linear dependence on the degree of ionization Z-N for fixed numbers of electrons N. The slopes and y intercepts associated with the linear dependence of ξ display marked shell-like behavior, while those associated with η vary rather smoothly with N. Our determinations of total energies are usually within 50 ppm of earlier Hartree-Fock calculations for those cases in which such calculations exist. Using the entire collection of energies and GSZ minimization parameters now available, we reexamine a modified version of the Thomas-Fermi statistical model (MTF) due to Green, Sellin, and Darewych. We show that this model is capable of yielding the linear Z-N dependence of the GSZ parameters which we found empirically in the MHF work. By numerical adjustment of the coefficients of our MTF model, we obtain energies of stable atoms and ions, as well as GSZ potential parameters which are in good agreement with the MHF calculations.