Relativistic Independent-Particle Model for Atoms, Based on Analytical Potentials

A two-parameter analytic potential for electrons in atoms, introduced by Green, Sellin, and Zachor, is used in conjunction with Dirac's equation to determine independent-particle-model electronic energy levels for neutral atoms in their ground states. The parameters are determined for each atom so that the predicted energy levels approximate observed electronic separation energies in accordance with a weighted least-squares sum. The agreement with experimental data is as good as for relativistic Hartree-Fock results. Electronic energies are given for a random selection of elements with $Z=10, 20, \dots , 90$.