We take account of the many-body dynamic interactions by including the wave-vector and frequency-dependent exchange-correlation (xc) kernel $f_{\mathrm{xc}}(\mathit{q},\omega )$ in the framework of the dielectric theory of the stopping power of crystals for moving charges. The cases of classical and quantum projectiles are considered. We find that (I) the role of the xc effects in slowing of charges in crystalline solids is more pronounced than it is within the jellium model and (II) for velocities below the stopping maximum, inclusion of xc leads to the improvement of the comparison of the theory with experiment over a range of solid targets. On the other hand, in the high-velocity regime, the role of the dynamic xc proves negligible, which does not contradict experiment, and which we substantiate analytically within the jellium model of the target. The input to our theory is the microscopic dielectric matrix ${\epsilon }_{\mathit{G}{\mathit{G}}^{\prime }}(\mathit{q},\omega )$ within the random phase approximation (i.e., with neglect of $f_{\mathrm{xc}}$), the calculation of which matrix is implemented in the existing solid-state codes.

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• Dielectric properties
• Stopping power
• Linear response theory
• Time-dependent DFT