To understand the magnetism of free atoms and ions, we may go through several stages, as follows, Hartree approximation - electrons are treated in a non-interactive manner. Beyond Hartree - interaction between electrons is taken into account. Spin-orbital coupling. Hyperfine interaction - the interaction between electrons and nucleus. Stage-1: At this stage, the single electron Schrodinger equation can be solved in the spherical potential field and one can get quantized energy levels indexed by quantum number $$n$$, $$l$$ and $$m$$. Hydrogen atom is the simplest and the most special case - the Coulomb potential is rigorously inverse proportional to $$r$$ and therefore energy levels with the same $$n$$ but different $$l$$ are degenerate. For general cases, e. g. hydrogen-like atoms, the effective Coulomb potential is not rigorously inverse proportional to $$r$$, as the result of screening effect from the atom core charge (nucleus + electrons). This results in the splitting o