  Monod and Beuneu [Monod and Beuneu, Phys. Rev. B 19, 911 (1979)] established
the validity of the Elliott-Yafet theory for elemental metals through
correlating the experimental electron spin resonance line-width with the
so-called spin-orbit admixture coefficients and the momentum-relaxation theory.
The spin-orbit admixture coefficients data were based on atomic spin-orbit
splitting. We highlight two shortcomings of the previous description: i) the
momentum-relaxation involves the Debye temperature and the electron-phonon
coupling whose variation among the elemental metals was neglected, ii) the
Elliott-Yafet theory involves matrix elements of the spin-orbit coupling (SOC),
which are however not identical to the SOC induced energy splitting of the
atomic levels, even though the two have similar magnitudes. We obtain the
empirical spin-orbit admixture parameters for the alkali metals by considering
the proper description of the momentum relaxation theory. In addition, we
present a model calculation which highlights the difference between the SOC
matrix element and energy splitting.
