Shape dependence of the conduction-electron spin-resonancegshift in a small sodium particle

A previous calculation of the size dependence of the conduction-electron spin-resonance $g$ shift for a small particle of sodium with cubic shape is extended to the case of a particle with spherical shape. Within a model where the conduction-electron wave functions are approximated by single orthogonalized standing waves, it is found that one of the major size-dependent contributions to the $g$ shift displays, for a spherical particle, the same qualitative size dependence as was obtained previously for a cubic particle. Specifically, we find that this term can be written as $\delta g\left(R\right)=[1-\beta (\frac{a}{R}\left)\right]\delta g\left(\infty \right)$, where $a$ is the lattice constant, $\beta$ is a parameter of the order of unity, $R$ is the radius of the spherical particle, and $\delta g\left(\infty \right)$ is the bulk $g$ shift.