Theory of Nuclear Quadrupole Interaction in Beryllium Metal

Abstract

The theory of the origin of the field gradient at nuclei in metals has been analyzed. The contributions of the ion cores and conduction electrons have been separately considered. In the case of beryllium metal, using orthogonalized plane wave functions, the conduction electrons are shown to enhance, by about eight percent, the field gradient due to the ion cores. Combining the results of our calculations with Knight's experimental value of 48 kc/sec for the ${\mathrm{Be}}^9$ coupling constant $\frac{e^2\mathrm{qQ}}{h}$, a value of $Q=0.032\mathrm{}\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$ is obtained. The dependence of the potential for the conduction electrons on the model chosen is analyzed in some detail. The various uncertainties in our field-gradient calculation and the theoretical value of the Knight shift in beryllium metal are discussed.