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 m_j of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (m_s unrestricted) and spin plus orbital polarized Hartree- Fock (m_s plus m_j unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, S_s(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.