X-ray emission and absorption edges of magnesium and aluminum

We have measured the edges of the $\mathrm{Mg} L_{2,3}$, $\mathrm{Mg} K\beta$, $\mathrm{Al} L_{2,3}$, and $\mathrm{Al} K\beta$ emission-band spectra and of the $\mathrm{Al} K$ absorption spectrum. The edges were analyzed in the light of the Mahan-Nozières-De Dominicis many-body theory. Threshold exponents obtained from absorption and emission data assuming a constant one-electron factor were ${\alpha }_0=0.2\mathrm{}\pm 0.06$ and ${\alpha }_1=0.0\mathrm{}\pm 0.08$ for Al, and ${\alpha }_0=0.3\mathrm{}\pm 0.07$ and ${\alpha }_1=-0.1\mathrm{}\pm 0.1$ for Mg. Allowance for Smrčka's one-electron calculations at the $L_{2,3}$ and $K\beta$ emission edges of Al significantly alters the value of ${\alpha }_0$ to 0.075 ± 0.05, causing it to disagree with the absorption exponent, and of ${\alpha }_1$ to 0.05 ± 0.05. The theoretical implications are discussed.