Kx-ray absorption in aluminum

The band structure of Al was obtained over a 4.2-Ry range from the bottom of the conduction band using the augmented-plane-wave (APW) method. The $K$ x-ray-absorption coefficient (and simultaneously the $K$-emission spectrum) was calculated with the inclusion of matrix elements using the APW wave functions. The energies were interpolated by a pseudopotential scheme. Structures in the unbroadened density of states and absorption coefficient were identified with critical points in the Brillouin zone. A comparison was made between the calculated absorption broadened by the appreciable $K$-level width and the measured spectra over a 22-eV range above threshold. The principal peak in the data at 5.5 eV is reproduced accurately by the calculations while a series of calculated peaks extending from 11 to 17 eV are not resolved in the measurements which exhibit a huge hump with its maximum at about 13 eV. It is shown that two weak peaks at about 1.4 and 2.4 eV above the edge cannot be explained in the one-electron approximation. We propose that they result from a two-electron process involving the excitation of a conduction as well as a core electron and the fact that there is structure in the density of states at about 1 and 2.5 eV below the Fermi level.