Band-Structure and Many-Body Effects in the Dynamical Response of Aluminum Metal

For many years, efforts to explain a double peak observed in the dynamical structure factor $S(\mathrm{q}; \omega )$ of aluminum—an archetype of jellium electronic behavior—via inelastic x-ray scattering have concentrated on many-body mechanisms for the uniform electron liquid. On the basis of a first-principles evaluation of $S(\mathrm{q}; \omega )$ for Al crystal we show that the double peak is an intrinsic feature of the response of noninteracting electron-hole pairs. Many-electron effects, in the form of a vertex correction for the irreducible polarizability, are found to substantially improve the agreement with experiment of the calculated loss intensities.