Quantum screened interactions in moderately dense plasmas and atomic contributions to thermodynamics

The screened Coulomb interaction phi through which particles interact in the path integral description of quantum plasmas is studied analytically and numerically. This interaction, which is a key ingredient in quantum Mayer diagrams, is closely related to the random-phase approximation potential known from finite-temperature many-body perturbation theory. An efficient way to compute numerically phi and its contributions in quantum Mayer diagrams under weak degeneracy conditions is proposed. Two key contributions to the thermodynamics of a moderately dense hydrogen plasma are studied using this method: polarization of the plasma and the electron-proton cluster function which accounts for the contributions from hydrogen atoms at finite density and finite temperature. The calculations include effects from dynamical screening and from shifts as well as broadening of spectral lines. When k lambda << 1, with k the inverse Debye screening length and lambda the electronic thermal de Broglie wavelength, a simple fast-to-evaluate approximation for phi can be used without loss of accuracy. The error induced on the electron-proton cluster function by the common approximation of replacing phi by a statically screened Debye potential is assessed for k lambda in the range 0 <= k lambda <= 0.5.