Dependence on ionization degree and relativistic effects in electron binding energies in free atoms and ions

The electron binding energy analysis proposed before for atoms is applied to positive free ions. As a result the binding energy self-similar dependence on atomic number and ionization degree of ions is shown up. The revealed scaling enables to compare electron binding energies in a large number of atoms and ions, manifests the relativistic spin-orbit interaction effect in heavy atoms and can be used for the new data verification. Оne can represent the orbital energies in filled shells of arbitrary many-electron atom or ion through two universal functions. The polynomial fit approximation of the last ones is constructed to estimate the binding energies in ions. The estimation can be used as initial value in more perfect computation and for rough calculation of the ionization cross section of many-electron atoms and ions by other particles.