Statistical Atom with Angular Momentum

By means of a variational principle, the method of Thomas and Fermi is extended, in a semiclassical manner, to atoms with a net total angular momentum. The resulting equation for the potential, which is valid for large angular momentum, is solved for small angular momentum, yielding approximate charge and current distributions for atoms in $P$ and $D$ states. Orbital magnetic hyperfine structure, and electric quadrupole hfs are calculated as a function of atomic number, and it is shown that the first is in approximate agreement with experiment.