Electron-Nuclear Interaction in Antimony Metal

Abstract

The field gradient at the nuclei due to the conduction electrons in antimony metal is calculated using an approximation for their wave functions in keeping with available information concerning the Fermi surface of antimony metal. It is shown that the Wannier functions for antimony can be closely approximated by a set of orthogonalized atomic orbitals (OAO) which are mixed by the noncentral terms in the one-electron Hamiltonian. The mixing of the $s$-like and $p$-like OAO is seen to be analogous to the concept of $s-p$ hybridization in the simple chemical picture of the solid. Combined with earlier calculations of the field gradient due to the ion cores, the total field gradient comes out as $eq=1998\mathrm{}\times {10}^{12}$ esu/${\mathrm{cm}}^3$ as compared to 1889×${10}^{12}$ esu/${\mathrm{cm}}^3$, the experimental value of the gradient based on Hewitt and Williams's quadrupole-resonance data and Murakawa's values of the quadrupole moments of the ${\mathrm{Sb}}^{121,123}$ nuclei. In addition, we have calculated the direct contributions to the isotropic and anisotropic Knight shifts from the spins of the conduction electrons near the Fermi surface. These are found to be ${\delta }_{\mathrm{iso}}=+0.07\%$ and ${\delta }_{\mathrm{ax}}=-0.05\%$. It is hoped that when experimental values of these quantities become available in the future a comparison with the theoretical values of the direct contributions will permit an assessment of the importance of other contributors to the Knight shift such as core polarization and orbital effects.