We present an investigation of the dynamic structure factor and of the dielectric function ${\epsilon }_M(\mathbf{Q},\omega )$ of the prototypical semiconductor silicon for finite momentum transfer, combining inelastic x-ray scattering experiments and ab initio calculations. In contrast with optical spectra, for finite momentum transfer time-dependent density-functional theory in the adiabatic local-density approximation together with lifetime broadening describes the physics of valence excitations correctly. Major structures in the spectra, governed by short-range crystal and exchange-correlation local-field effects, are strongly influenced by a mixing of transitions of positive and negative energies, in striking difference to spectra for vanishing momentum transfer. This mixing gives rise to a pronounced Fano asymmetry.

• Received 23 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.237602