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Electron-ion and ion-ion potentials for modeling warm-dense-matter: applications to laser-heated or shock-compressed Al and Si

The pair-interactions U_{ij}(r) determine the thermodynamics and linear transport properties of matter via the pair-distribution functions (PDFs), i.e., g_{ij}(r). Great simplicity is achieved if U_{ij}(r) could be directly used to predict material properties via classical simulations, avoiding many-body wavefunctions. Warm dense matter (WDM) is encountered in quasi-equilibria where the electron temperature $T_e$ differs from the ion temperature T_i, as in laser-heated or in shock-compressed matter. The electron PDFs g_{ee}(r) as perturbed by the ions are used to evaluate fully non-local exchange-correlation corrections to the free energy, using Hydrogen as an example. Electron-ion potentials for ions with a bound core are discussed with Al and Si as examples, for WDM with T_e \ne T_i, and valid for times shorter than the electron-ion relaxation time. In some cases the potentials develop attractive regions, and then become repulsive and `Yukawa-like' for higher $T_e$. These results clarify the origin of initial phonon-hardening and rapid release. Pair-potentials for shock-heated WDM show that phonon hardening would not occur in most such systems. Defining meaningful quasi-equilibrium static transport coefficients consistent with the dynamic values is addressed. There seems to be no meaningful `static conductivity' obtainable by extrapolating experimental or theoretical σ(ω, T_i, T_e) to ω\to 0, unless T_i \to T_e as well. Illustrative calculations of quasi-static resistivities R(T_i,T_e) of laser-heated as well as shock-heated Aluminum and Silicon are presented using our pseudopotentials, pair-potentials and classical integral equations. The quasi-static resistivities display clear differences in their temperature evolutions, but are not the strict ω\to 0 limits of the dynamic values.