Hydrodynamic theory for ion structure and stopping power in quantum plasmas

We present a theory for the dynamical ion structure factor (DISF) and ion stopping power in an unmagnetized collisional quantum plasma with degenerate electron fluids and nondegenerate strongly correlated ion fluids. Our theory is based on the fluctuation dissipation theorem and the quantum plasma dielectric constant that is deduced from a linearized viscoelastic quantum hydrodynamical (LVQHD) model. The latter incorporates the essential physics of quantum forces, which are associated with the quantum statistical pressure, electron-exchange, and electron-correlation effects, the quantum electron recoil effect caused by the dispersion of overlapping electron wave functions that control the dynamics of degenerate electron fluids, and the viscoelastic properties of strongly correlated ion fluids. Both degenerate electrons and nondegenerate strongly correlated ions are coupled with each other via the space charge electric force. Thus, our LVQHD theory is valid for a collisional quantum plasma at atomic scales with a wide range of the ion coupling parameter, the plasma composition, and plasma number densities that are relevant for compressed plasmas in laboratories (inertial confinement fusion schemes) and in astrophysical environments (e. g., warm dense matter and the cores of white dwarf stars). It is found that quantum electron effects and viscoelastic properties of strongly correlated ions significantly affect the features of the DISF and the ion stopping power (ISP). Unlike previous theories, which have studied ion correlations in terms of the ion coupling parameter, by neglecting the essential physics of collective effects that are competing among each other, we have here developed a method to evaluate the dependence of the plasma static and dynamical features in terms of individual parameters, like the Wigner-Seitz radius, the ion atomic number, and the ion temperature. It is found that due to the complex nature of charge screening in quantum plasmas, the ion coupling parameter alone cannot be a good measure for determining ion correlation effects in a collisional quantum plasma, and such a characteristic of a dense quantum plasma should be evaluated against each of the plasma parameters involved. The present investigation thus provides testable predictions for the DISF and ISP and is henceforth applicable to a wide range of compressed plasma categories ranging from laboratory to astrophysical warm dense matter. DOI: 10.1103/PhysRevE.87.043106