  We report a calculation of the Sternheimer anti-shielding factor, \gamma, by
means of first order perturbation theory. In quality of basis functions, we use
Hartree-Fock electronic orbitals, expanded on hydrogenic atomic states. The
computed \gamma(r) for Fe^{3+} and Cu^{1+} inner electronic cores are reported
and compared with literature values, obtained from alternative methodologies.
