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For the diagnostics of dense plasmas, photons in the vacuum ultraviolet (VUV) or X-ray domain are required. First experiments have demonstrated the great capacity of X-ray Thomson scattering for the determination of plasma parameters such as density, temperature, and ionization state. For a reliable interpretation of the experimental data, the interaction of energetic photons with the plasma has to be considered. The cross section for Thomson scattering is related to the dynamic structure factor S(k,ω). We improve the usual random phase approximation by including collisions and calculate a dynamic collision frequency in Born approximation. We also study the influence of dynamic screening and the relation to the concept of dynamic local-field corrections to the dielectric function. We give results for a variety of plasma parameters and determine the region where collisions are of relevance.