Attenuation of Friedel oscillations in some metals

The asymptotic expansion of the metallic ion-ion potential is reformulated, in the local form, in terms of the self-consistent dielectric function of Singwi et al. up to terms of order $r^{-5\mathrm{}}$. The evaluation of this expansion reveals that, in the alkalis except for lithium, the "Friedel oscillations" are negligible and are replaced by higher-order terms mostly in $\frac{cos\left(2\mathrm{}{k}_{F}r\right)}{r^5}$. For magnesium and aluminum, however, the Friedel term is still the dominant one.