In a previous paper, a method was presented for determining, within the framework of the unrestricted Hartree-Fock formalism, the contribution of closed atomic shells (called Sternheimer antishielding) to magnetic and electric hyperfine interactions. We here discuss and apply this method to the study of the antishielding of both magnetic dipole and electric quadrupole interactions associated with the aspherical valence electrons of atoms and ions. In addition to closed shell antishielding, it is shown that there are repercussions within the open shell which are significant for hyperfine interactions. Results of specific computations for the free Fe2+ ion and the Cl atom are given, and comparisons are made with earlier perturbation theory results. An estimate is made of the quadrupole moment of the excited state of Fe57. Finally, the serious symmetry problem, which is associated with polarization investigations applied either to atoms or solids, is discussed.