Wave-vector- and frequency-dependent dielectric matrix for aluminum: Energy-loss spectra

A previous calculation of the dielectric matrix in aluminum in the static limit is extended to include the frequency dependence. Exchange and correlation corrections to the random-phase results are studied according to three different approximations. The values of $\mathrm{Im}{\left[{\epsilon }^{-1\mathrm{}}\right(k,\omega \left)\right]}_{11}$, responsible for the electron-energy-loss cross sections, are computed and compared with the experimental results of Petri and Otto. The results do not depend significantly on the form of exchange-correlation corrections employed.