The Dynamical Structure Factor (DSF) is a key observable in high energy density science that is directly measured e.g. using inelastic x-ray scattering techniques [1]. The DSF delivers a wealth of information about macroscopic equation of state data (temperature of electrons and of ion species, average ionization
states, electron density), collective and single-particle dynamics, static correlations, electron-ion collisions, and electronic structure. In a strongly coupled, partly degenerate many-body system, such as warm dense matter (WDM) generated by intense laser-matter interaction and shock wave compression, calculations of the
DSF are a formidable task. Ab-initio simulations of the DSF in WDM are currently not feasible on reasonable time scales and one has to resort to analytical and semianalytical approaches. In this talk, I present the state of the art theoretical framework for DSF calculations in the context of x-ray scattering plasma diagnostics [2, 3, 4]. The theoretical foundation is given by the generalized linear response theory in the Zubarev formulation [5], which allows to calculate the dynamical response of a given quantum statistical ensemble to external fields, such as x-ray photons. The DSF or two-particle correlation function is expressed via many-body Green
functions and calculated by aid of Feynman diagrams and partial summations to achieve a self-consistent treatment of field propagators and self-energies. The resulting expressions are identifi ed with the components of the Chihara separation [6] of the DSF into free-free, bound-bound, and bound-free processes and suitable approximations for each process can be given. The predictive and analytical strength of this approach will be
demonstrated using recently obtained experimental data which led to novel insights in high energy density science. Novel directions in DSF calculations are explored by combining ab-initio methods such as finite temperature-density functional theory-molecular dynamics simulations with the aforementioned semianalytical approaches.
Some applications of this hybrid technique, their advantages and issues will be discussed. In parallel, a fully self-consistent many-body theoretical treatment is developed in order to provide solid and reliable benchmarks and limiting cases for simulation methods. References [1.] Glenzer, S. H. and Redmer, R., X-ray Thomson scattering in high energy density plasmas, Rev. Mod. Phys. 81, 1625{1663 (2009). [2.] Gregori, G, Glenzer, S. H., and Landen, O. L., Generalized x-ray scattering cross section from nonequi-
librium plasmas, Phys. Rev. E 74, 26402 (2006). [3.] Redmer, R, Reinholz, H, Ropke, G, Thiele, R, and Holl, A, Theory of X-ray Thomson scattering in dense plasmas, IEEE T. Plasma. Sci. 33, 77{84 (2005). [4.] Fortmann, C., Wierling, A., and Ropke, G., In
uence of local- field corrections on Thomson scattering in collision-dominated two-component plasmas, Physical Review E 81, 26405 (2010).
[5.] Zubarev, D, Morozov, V, and Ropke, G, Statistical Mechanics of Nonequilibrium Processes, (Akademie Verlag, Berlin, 1996). [6.] Chihara, J., Interaction of photons with plasmas and liquid metals-photoabsorption and scattering, J. Phys.: Condens. Matter 12, 231 (2000).
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