Equation of state for weakly coupled quantum plasmas J. Vorberger, M. Schlanges, W.D. Kraeft Institut f¨ ur Physik der Ernst-Moritz-Arndt-Universit¨ at Greifswald, 17487 Greifswald, Germany Starting from quantum statistical theory [1] we estab- lish a perturbation expansion for the equation of state of a quantum plasma in terms of the dynamically screened potential. In order to describe two component plasmas of any degeneracy, we restrict ourselves to systems of weak coupling and take into account terms up to order e 4 [2]. 20 22 24 26 28 log 10 n (cm -3 ) 0.6 0.7 0.8 0.9 1.0 1.1 p/p 0 DH T=0 MW e 4 T=10 5 K T=10 6 K T=10 7 K Figure 1: Isotherms of the pressure of an electron gas in units of the ideal pressure as function of the number density in different approximations. Results for an electron gas are shown in figure 1. DH means the classical Debye–Hueckel correction, MW takes into account Hartree-Fock(HF) and Montroll-Ward(MW) terms, and the e 4 curve additionally accounts for exchange effects of order e 4 and represents the full expansion up to this order. The minimum behavior of the lines at interme- diate density is due to nonideality effects. At higher and lower densities the curves approach unity what is caused by degeneracy effects at high densities and by large inter- particle distances at low densities. 18 20 22 24 26 28 log 10 n (cm -3 ) 0.4 0.6 0.8 1.0 1.2 p/p 0 DPIMC WPMD DH T=0 MW e 4 T=1 10 5 K r s =1 n 3 =1 =1 Figure 2: Pressure of a fully ionized hydrogen plasma in units of the ideal pressure as function of the number density at a temperature of T = 10 5 K in different approximations. WPMD data from [3], DPIMC data from [4]. The pressure of fully ionized hydrogen can be seen in figure 2. The curves for hydrogen show, in principle, the same behavior as the curves in figure 1. We compare our results with results from first principle numerical simu- lations: Direct Path Integral Monte Carlo [4] and Wave Packet Molecular Dynamics [5]. As can be seen in this fig- ure, at lower densities the agreement between the results is rather good. The results for depth and exact location of the pressure minimum strongly depend on the technique and thus on the approximation used. 21 22 23 24 25 log 10 n (cm -3 ) 0 20 40 60 80 100 U/N [eV] WPMD PIMC MW e 4 Pade T=125000K Figure 3: Internal energy of a fully ionized hydrogen plasma as function of the number density n at a temperature of T =1.25×10 5 K in different techniques. WPMD data from [5], PIMC data from [6]. Pad´ e means a Pad´ e formula [1]. Nearly the same situation can be observed in figure 3 where the internal energy for hydrogen is shown. At inter- mediate and higher densities, where the coupling parame- ter becomes equal to or larger than unity strong electron– proton and proton–proton correlations occur. These cor- relations are not included in our approach. References [1] W.D. Kraeft, D. Kremp, W. Ebeling and G. R¨ opke, Quantum Statistics of Charged Particle Systems, Akademie–Verlag, Berlin (1986). [2] J. Vorberger, M. Schlanges, W.D. Kraeft, Phys. Rev. E, accepted for publication. [3] M. Knaup, private communication. [4] V.S. Filinov, M. Bonitz, W. Ebeling, V.E. Fortov, Plasma Phys. Control. Fusion 43, 743 (2001); V.S. Filinov, private communication. [5] M. Knaup, P.-G. Reinhard, C. Toepffer, Contr. Plas. Phys. 41, 159 (2001) [6] B. Militzer, PhD, University of Illinois, Urbana, 2000; B. Militzer, D.M. Ceperley, Phys. Rev. E 63, 066404 (2001).