Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas

Extending bur previous work [A.V Filinov et al., J. Phys. A 36, 5957 (2003)], we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: (i) the diagonal Kelbg potential, (ii) the off-diagonal Kelbg potential, (iii) the improved diagonal-Kelbg potential, (iv) an effective potential obtained with the Feynman-Kleinert variational principle, and (v) the "exact" quantum pair potential derived from the two-particle density matrix. For the improved diagonal Kelbg potential, a simple temperature-dependent fit is derived which accurately reproduces the "exact" pair potential in the whole temperature range. The derived pseudopotentials are then. used in path integral Monte Carlo and molecular-dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about 60 000 K. Finally, we point out an interesting relationship between the quantum potentials and the effective potentials used in density-functional theory.