A new method is developed for determining the distortions (polarizabilities) induced in electronic distributions by valence electrons and/or crystalline fields and their effect (expressed as Sternheimer shielding factors) on magnetic and electric hyperfine interactions. For illustrative purposes emphasis is placed in this paper on the calculation of Sternheimer antishielding factors (${\ensuremath{\gamma}}_{\ensuremath{\infty}}$). Working within the framework of the Hartree-Fock self-consistent field formalism, it is shown that the `angular' excitations are gotten by relaxing the usual restriction that the spatial part of the one-electron functions be separable into a radial function times an angular function; relaxing the restriction that electrons of the same shell but differing in magnetic quantum number (${m}_{l}$) have the same radial function yields the `radial' excitations. To illustrate the method, calculations are reported for several spherical ions (${\mathrm{Cl}}^{\ensuremath{-}}$ and ${\mathrm{Cu}}^{+}$) in an external field, but the scheme is also applicable to the problem of induced electric quadrupole (and magnetic dipole and higher multipole) distortions of an ion by its own aspherical charge distribution. The problems of orthogonality, exchange, and self-consistency, which have complicated applications of the perturbation method are easily resolved by this approach. Further, since a self-consistent field procedure is followed, the distortions induced in the inner closed shells by the distorted outer shells are included in a natural way and by comparison with the results of the perturbation-variation method (which does not take these into consideration) these additional effects are shown to be significant.