Volume dependence of the Knight shift in lithium

This work is to confirm a significant discrepancy between the calculated volume dependence of $〈{\left|\psi \mathrm{}\right(0\left)\right|}^2〉$ in Li metal and the corresponding quantity deduced from experimental results using a simple equation for the Knight shift, $K=\left(\frac{8\pi }{3}\right){\chi }_P\Omega 〈{\left|\psi \mathrm{}\right(0\left)\right|}^2〉$. Here $〈{\left|\psi \mathrm{}\right(0\left)\right|}^2〉\equiv P_F$ is the amplitude of the conduction-electron wave function averaged over the Fermi surface. ${\chi }_P$ and $\Omega$ are the Pauli susceptibility and the atomic volume, respectively. The experimental determination of $〈{\left|\psi \mathrm{}\right(0\left)\right|}^2〉$ was obtained from an old measurement of $K$ [G. B. Benedek and T. Kushida, J. Phys. Chem. Solids 5, 241 (1958)] and a recent measurement for ${\chi }_P$ [Toshimoto Kushida, J. C. Murphy, and M. Hanabusa, Phys. Rev. B 13, 5136 (1976)]. Both quantities $K$ and ${\chi }_P$ were measured as a function of volume. It was felt important to repeat the old Knight-shift experiment, since the experiment requires an accurate resonance-frequency measurement (≃one part in ${10}^7$), which was marginal 20 years ago, and a resolution of the discrepancy is essential to the understanding of the electronic structure of a simple metal. The present measurement is one order of magnitude more accurate and indicates a small systematic error in the previous data. The conclusion is, however, essentially unchanged; an electron polarization enhancement seen by the Li nucleus in Li metal is almost independent of the volume change, contrary to an intuitive model which predicts $\frac{d\ln P_F}{d\ln V}=-1\mathrm{}$. Recent calculations show that the core-polarization effect $P_F^{\mathrm{cp}}$ is important for Li and that $P_F^{\mathrm{cp}}$ has a large volume dependence. The Knight-shift equation should be modified to $K=\left(\frac{8\pi }{3}\right){\chi }_P\Omega (P_F+P_F^{\mathrm{cp}})$. The volume dependence of $P_F$ is almost canceled by that of the $P_F^{\mathrm{cp}}$.