Relativistic self-consistent-field calculations of the hyperfine structure in the 3d -shell atoms

Nonrelativistic and relativistic self-consistent-field wave functions of the Hartree-Fock type and with statistical exchange have been used for the calculation of radial hyperfine integrals for the $3d$-shell atoms within the 3dN+14s and 3dN+2 configurations. The mean value of r^-3 for the $3d$ electron and the electron density at the nucleus for the $4s$ electron have been evaluated with the nonrelativistic wave functions. The relativistic wave functions have been used for the calculation of radial integrals appearing in an effective hyperfine Hamiltonian for the magnetic dipole and electric quadrupole interaction. For the magnetic dipole interaction the relativistic wave functions calculated with a statistical exchange potential are found to describe the hyperfine interaction for the $4s$ electron in a better way than what is achieved with the HF potential. The experimental orbital, spin-dipole, and contact radial parameters for the $3d$ electrons of some of the elements seem to be strongly influenced by configuration-interaction effects, which are not included in our theoretical values. The magnitude of configuration-interaction effects has been estimated for the orbital and spin-dipole parts by comparing existing experimental radial integrals with the corresponding relativistic ones. The pure relativistic parameters in the effective Hamiltonian for the quadrupole interaction are found to be in good agreement with the experimental values for manganese and cobalt, while the experimental uncertainty for the parameters of the other elements is still too large for a critical comparison to be done. Quadrupole moments have been evaluated with the use of published experimental hyperfine parameters and theoretical radial integrals calculated in this work. A comparison between ratios of experimental quadrupole parameters and relativistic ones gave an estimate of the quadrupole shielding, known as the Sternheimer effect.