gValue in Alkali-Metal Conduction-Electron Spin Resonance

A method for examining the convergence of expansions of wave functions for nearly free electrons is presented. It is shown that Bardeen-type expansions of alkali-metal conduction-electron wave functions converge sufficiently slowly so that it is necessary, when calculating the value of a physical quantity to any given power of k, to include all terms of all orders in $u(\mathrm{k},\mathrm{r})$ which contribute to that power. Consequently, wave-function expansions to third order in k which include the effects of spin-orbit interaction to first order are derived, in the spherical approximation, for these metals. Using these wave functions in Yafet's equation, the $g$ shift, to second order in|k| is expressed in terms of radial wave functions. The radial functions are evaluated numerically using the quantum defect nethod under four different approximations: (i) With and without the so-called "polarization correction" and (ii) with and without a term in the potential corresponding to an approximate self-consistent Hartree field due to the presence of other conduction electrons within the Wigner-Seitz sphere. The best agreement with experiment is obtained when the "polarization correction" is neglected and the Hartree term included. In this approximation the effective mass ratio, $\frac{m}{{m,}^{*}}$ is considerably closer to unity in the heavier alkali metals than was predicted by earlier calculations. The "polarization correction" is examined in detail in an unsuccessful effort to determine why it leads to a considerable decrease in the agreement with experiment.