Unrestricted Dirac-Fock theory: relativistic determination of core polarization hyperfine interactions

The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection msub(j) of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (msub(s) unrestricted) and spin plus orbital polarized Hartree-Fock (msub(s) plus msub(l) unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, Ssub(s)(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (approximately 6) found earlier for these same ions. Comparison is made with the limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment. (Auth.)