Core-Polarization Contribution to the Knight Shift in Beryllium Metal

Direct and core-polarization contributions to the Knight shift in beryllium metal were calculated at a number of symmetry points near the Fermi surface. The direct contribution was evaluated using wave functions for the conduction electrons by the orthogonalized-plane-wave method. The contribution of the core electrons was determined using the moment-perturbation (MP) method developed in an earlier paper. The accuracy of the MP method was rechecked by calculating the core contribution to the hyperfine coupling constant in the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ state of the beryllium atom. Good agreement was obtained with the result of an earlier self-consistent-field calculation by Goodings. For the ${{\Gamma }_4}^{-}$ level, the direct and core contributions to the Knight shift are 0.01536 and 0.00258%, respectively. For the two degenerate levels of $H_1$, the direct contributions both vanish while the core-polarization contributions are -0.00061 and -0.00001%. These results lead to the conclusion that core-polarization effects alone can not explain the near-vanishing Knight shift observed experimentally in beryllium metal. Some other contributions such as those from various orbital mechanisms would therefore have to be considered.