X-Ray Edges of Simple Metals: Dependence on Electron Density

Abstract

Data analyses reveal that the Mahan form of the x-ray absorption threshold law, ${\epsilon }_2\left(\omega \right)=A{\left[\frac{(\hslash \omega -\hslash {\omega }_T)}{\xi }\right]}^{-{\alpha }_0}$, can describe $L_{2,3}$ edge data of Al, Mg, and Na, with the empirical rule ${\alpha }_0\approx 0.068{\mathcal{r}}_s$. However, the many-electron interpertation of the Li $K$ edge cannot be reconciled with this rule, and the exponents ${\alpha }_0$ can be calculated from the Nozières-De Dominicis expression only if the electron-hole interaction exhibits unusual properties.