Proceedings of the International Conference on the Physics of Strongly Coupled. Plasma in Binz 1995, Editors W. D. Kraeft, M. Schlanges, World Scienti c, 1995.
To appear in: Proceedings of the International Conference on the Physics of Strongly Coupled Plasma in Binz 1995, Editors W. D. Kraeft, M. Schlanges, World Scienti c, 1995.
CORRELATION FUNCTIONS AND THERMODYNAMICS OF PARTIALLY IONIZED NONIDEAL PLASMAS WERNER EBELING, DIETER BEULE, ANDREAS FORSTER, and MICHAEL KASCH
Institut fur Physik, Humboldt-Universitat zu Berlin, Invalidenstrae 110, D-10115 Berlin, Germany
Abstract
Classical HNC equations are used to calculate correlation functions and thermodynamic properties of quantum plasmas. Many-particle correlation and exchange e ects are taken into account via e ective potentials obtained from the Slater sum method. The results are compared with data from Pade approximations for the chemical picture (PACH) as well as with recent results from path integral Monte Carlo simulations. We investigate the behavior of the entropy and the adiabatic equation of state.
1 Introduction: Physical and Chemical Picture Physical and chemical pictures provide alternative descriptions of plasmas. The only constituents in the physical picture are electrons and nuclei. All other particles, e.g., atoms, ions, and molecules are considered as composites build from electrons and nuclei. The great advantage of the physical picture is its structural simplicity: All matter, independent of its state of ionization is considered as a system of point charges with Coulomb interactions. Masses, charges, and abundancies of nuclei are the only input of the theory. The chemical picture1 uses a much more complicated model of a plasma. In this model the atoms, ions, and molecules are treated as separate species. Therefore the constituents of the plasma are free electrons, free nuclei, ions, atoms, and molecules. All species are treated on equal footing (principle of particle democracy). The advantage of the chemical picture is that it is in many cases more appropriate for the description of real plasma2 . It re ects the simple fact, that in many respects atoms and molecules behave as point masses/charges and the internal structure is rather irrelevant. The chemical picture is quite successful for applications but it needs a careful quantum-statistical analysis in order to avoid double counting of e ects.
2 Slater Sums, E ective Potentials, and Correlation Functions The method of Slater sums goes back to Morita3 and was worked out by Kelbg and his school in the sixties at the Rostock University (Kelbg4 , Ebeling5 , Kraeft and
Kremp6 ). One starts out from the Slater sum S (N ) (r1 ; : : : ; X rN ) = 3 N N ! < r1; 1 ; : : : ; rN ; N j exp (? HN ) j r1 ; 1; : : : ; rN ; N > ; (1) i
where HN denotes the Hamiltonian and the thermal de Broglie wavelength and = kB T The summation extends over the spins states. The Slater sum is an analogue of the classical Boltzmann factor and one de nes therefore an e ective potential by X X uij + uijk + : : : U (N ) (r1 ; : : : ; rN ) = i
