gShift of Conduction Electrons in Sodium

A simple procedure for estimating the wave-vector-dependent $g$ shift of conduction electrons in sodium metal is described. The conduction-electron wave functions are approximated by single orthogonalized plane waves (SOPW), orthogonal to the $2p$, $2s$, and $1s$ ion-core wave functions. All the core wave functions are determined variationally in terms of a two-parameter ion-core potential. The binding energy and spin-orbit splitting of the $2p$ core state are adjusted to experimental values. It is found that the core functions have negligible amplitude at the boundary of the cellular polyhedron. The $g$ shift is then approximately given by $\frac{2}{\hslash }$ times the expectation value of the orbital angular momentum in a unit cell, plus two small relativistic terms. The calculated Fermi-surface average of the $g$ shift is -5×${10}^{-4\mathrm{}}$. Since the experimental values are (-6±2)×${10}^{-4\mathrm{}}$, (-8±2)×${10}^{-4\mathrm{}}$, and (-10±2)×${10}^{-4\mathrm{}}$, it is concluded that a large part of the $g$ shift in sodium can be accounted for by using the SOPW method.