Dynamical structure factor of CaF$_{2}$: Striking coherent dynamical screening of ``atomic'' Ca-derived excitations

We report \textit{ab initio} calculations of the dynamical structure factor of CaF$_{2, }$performed within time-dependent density functional theory, together with non-resonant inelastic x-ray scattering measurements. The ``effective'' dielectric function has also been determined. The excitations derived from the ``atomic'' Ca 3p--$>$ 3d process display a striking wave vector dependence. Such dipole-allowed excitation would be expected to lie at about 27 eV. \textit{However, for small q's the leading Ca 3p--$>$ 3d feature lies at about 35 eV.} We demonstrate that this feature corresponds to a collective mode, whose physics embodies a remarkable manifestation of crystal local-field effects induced by charge localization and their interplay with the dynamical screening at the ``natural'' 3p--$>$ 3d energy. For intermediate $q's$, the 27 eV excitation emerges and coexists with the collective mode ---thus highlighting the physics of the ``atomic'' 3p--$>$3d excitation in the condensed matter environment, which is controlled by dynamical coherent screening. For large $q's$ the Ca-derived spectrum consists of the ``single-particle'' Ca 3p--$>$3d excitation, together with the dipole-forbidden Ca 3s--$>$3d excitation.