Many-particle effects at core thresholds in simple metals

We have analyzed inelastic electron-scattering (IES) data at the Na ${\mathit{L}}_{2,3}$ and K ${\mathit{M}}_{2,3}$ thresholds in terms of the Mahan-Nozières–De Dominicis (MND) model. We have also obtained the absorption coefficient μ and imaginary dielectric function ${\mathrm{\epsilon }}_2$ from the IES data and analyzed them in the same manner as the raw data. For K the peaking parameter ${\mathrm{\alpha }}_0$ obtained from absorption depends upon whether IES data, μ, or ${\mathrm{\epsilon }}_2$ is used. For Na, ${\mathrm{\alpha }}_0$ does not vary significantly among the three absorption spectral functions and has a value of 0.22±0.03 if uncertainties in the transition density of states are included. Exchange mixing is found to be a small effect at the Na ${\mathit{L}}_{2,3}$ absorption edge. We have reanalyzed published p-core soft-x-ray emission data from Na and K and account for the effects of partial phonon relaxation on ${\mathrm{\alpha }}_0$. In both cases ${\mathrm{\alpha }}_0$ is significantly less than for the corresponding absorption spectra with values of about 0.15. We have also reanalyzed published Na core-level x-ray photoemission spectroscopy data including surface contributions and for the appropriate exponent obtain α=0.22±0.02. The results above taken in concert indicate a failure in the presently accepted MND model. We suggest that previously unconsidered dynamical effects must be included.