Comment on the Hartree-Fock theory for hyperfine interactions

Recently Amoruso and Johnson (AJ), using a relativistic formulation, have pointed out that earlier theories of exchange-polarization effects on hyperfine constants in atoms had omitted an important contribution. This contribution would have serious implications for a number of solid-state hyperfine calculations. We show that in a correct Hartree-Fock formulation, the contribution proposed by AJ vanishes exactly, a conclusion that is also substantiated by results of recent many-body perturbation-theory calculations. The need for a reevaluation of relativistic effects on exchange core polarization in Hartree-Fock theory is emphasized.