Analytic electron-ion effective potentials forZ≤55

Abstract

Analytic $Z$-dependent electron-ion potentials have been obtained for all isoelectronic sequences from He to Cs. These potentials have a parametrized Yukawa component for each electron shell. Parameter values were determined by iteratively solving the Dirac equation until a match with experimental ionization energies was obtained. The screening parameters for each isoelectronic sequence were fit to simple $Z$-dependent functions. Working systematically through the periodic table and using preceding fits to obtain the screening parameters for closed inner shells, I found it necessary to evaluate only the screening parameter for the valence shell of the parent ion. Excited states having the same parentage as the ground state are also given to good accuracy by these potentials. The energy offset of excited states having a different parentage than the ground state is obtained from simple $Z$-dependent functions.