Hyperfine field in metallic iron: An appraisal of the theory

Abstract

Recently an experiment has been performed for the first time to measure the contribution to the hyperfine field in metallic iron from each electron shell separately. It view of this measurement, it has become important to study the interrelationship between various theories for studying exchange core polarization contributions to the hyperfine field with the aim of deciding on the appropriate theoretical values that have to be compared with experimental data. Such a comparison is carried out here between the Hartree-Fock perturbation theory, self-consistent-field perturbation theory, linked-cluster many-body perturbation theory (LCMBPT), and the unrestricted Hartree-Fock (UHF) theory. It is concluded that, in principle, the predictions of the self-consistent-field perturbation theory and UHF theory for shell-by-shell contributions should be comparable, although the total hyperfine fields from all the shells should be the same for all four theories. The quantitative accuracies of the various procedures are studied by considering the results for ${\mathrm{Fe}}^{+3}$ ion, ion atom, and manganese atom. It is concluded that while the accuracies of results from the Hartree-Fock and self-consistent-field perturbation theory and LCMBPT are comparable, there are some numerical problems in obtaining comparable accuracy with the UHF procedure. Shell-by-shell core contributions and conduction-band contributions to the hyperfine field are compared with the results from internal-conversion experiments. A possible reason for differences between theory and experiment is discussed.