Theory of Core-Electron Contributions to Hyperfine Interactions

Abstract

A convenient method is devised for the calculation of magnetic hyperfine constants in atoms, molecules, and metals taking into consideration the exchange interaction between the core electrons and the unpaired valence electrons. In this method, the core-electron wave functions are perturbed by the nuclear magnetic moment via the Fermi contact term, and the energy of the system is then calculated in the Hartree-Fock approximation using the perturbed core wave functions. The present method is closely related to the exchange perturbation method of Cohen, Goodings, and Heine. However, the former has the advantage of being more flexible in the sense that the same perturbed core-electron functions may be used for the ground and excited states of the atom and for metals without significant error. For lithium atom $1{s}^{2}2s$ and $1{s}^{2}2p$ states, we obtained values for the core contribution to the hyperfine constant $a$ (in aI\ifmmode\cdot\else\textperiodcentered\fi{}S) of 83.76 Mc/sec and -8.9 Mc/sec in good agreement with the earlier values of Cohen, Goodings, and Heine. We have applied this method to a calculation of the core-polarization correction to the Knight shift in lithium metal using recent wave functions of Kohn and Callaway. The core-polarization corrections produced by the $s$ and $p$ parts of the conduction-electron wave function are nearly equal but opposite in sign, while that produced by the $d$ part is an order of magnitude smaller. This results in a net correction of about -5.3% of the direct contribution to the Knight shift from the conduction electrons.