Theory of nuclear quadrupole interaction in hexagonal close packed metals—cadmium and zinc

The conduction-electron contribution to the electric field gradient has been calculated for zinc and cadmium. From a study of the conduction and core electron distributions relative to each other, it is concluded that different components of the field gradient due to the conduction electrons, such as from the local and planewave components of the conduction-electron densities, should be shielded differently. A value of about $\frac{{\gamma }_{\infty }}{2}$ is estimated for the field gradient due to the plane-wave component of the density. Using the calculated field gradients in the two metals, the quadrupole moments of ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ are obtained as 0.50 and 0.76 b, the latter being in good agreement with the value derived earlier from ionic crystal measurements. The effect of the larger antishielding factor on the earlier calculated field gradients in beryllium and magnesium is discussed and it is concluded that the earlier good agreement between theory and experiment for these metals is not significantly affected. Finally, the bearing of the results of the present work on the empirical correlation obtained recently between the conduction-electron and lattice contributions is discussed.