Contrib. Plasma Phys. 45, No. 3-4, 258 – 265 (2005) / DOI 10.1002/ctpp.200510029 Thermodynamics of Hydrogen and Hydrogen-Helium Plasmas: Path Integral Monte Carlo Calculations and Chemical Picture V. S. Filinov ∗1 , P. R. Levashov 1 , M. Bonitz 2 , and V. E. Fortov 1 1 Institute for High Energy Density, Russian Academy of Sciences, Izhorskaya 13/19, Moscow 125412, Russia 2 Christian-Albrechts-Universit¨ at zu Kiel, Institut f¨ ur Theoretische Physik und Astrophysik, Leibnizstr. 15, 24098 Kiel, Germany Received 3 February 2005, accepted 20 March 2005 Published online 13 June 2005 Key words Path integral Monte Carlo, Chemical picture, Hydrogen-helium plasma, Plasma phase transition. PACS 52.25.Kn, 52.65.Pp In this paper we study thermodynamic properties of hydrogen and hydrogen-helium mixtures with the help of the direct path integral Monte Carlo simulations. The results are compared with available theoretical and experimental methods based, in particular, on chemical picture. We investigate the effects of temperature ionization in low-density hydrogen plasma. We also present a number of calculated isotherms for hydrogen- helium mixture with the mass concentration of helium Y =0.234 in the range from 10 4 K to 2 · 10 5 K. In the density region where a sharp conductivity rise have been observed experimentally the simulations give indications for one or two plasma phase transitions, in accordance with earlier theoretical predictions. c  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction Many astrophysical problems require the knowledge of thermodynamic properties of hydrogen and helium [1–5]. To understand different effects in stellar structure and evolution one should provide accurate modelling of the underlying physics including equation of state (EOS) effects. In normal stars where plasma is fully-ionized and almost ideal the construction of EOS doesn’t reveal particular difficulties. However the investigation of the giant planets Jupiter and Saturn, and to a lesser extent brown dwarfs demands thermodynamic information for hydrogen and helium in the approximate range of temperatures 10 3 K <T< 10 5 K and mass densities 0.01 < ρ< 100 g/cm 3 . In this region the complexity of an EOS calculation increases considerably when nonideal effects are compounded with chemical reactions associated with partial pressure dissociation and ionization equilibria [6–10]. Moreover, in this region the the so-called plasma phase transition (PPT) has been predicted [9, 10]. Significant efforts have been made in the last decades to understand the behaviour of dense fully-ionized and partially-ionized hydrogen and helium (see, for example, [8] and references therein). In these works mostly the chemical picture is applied for the calculation of thermodynamic properties. The chemical picture assumes that bound configurations, such as atoms and molecules, retain a definite identity and interact through pair potentials; in other words, this model is valid only at weak interparticle interactions. However at densities corresponding to pressure ionization the electrons in bound configurations become delocalized and bound species lose their definiteness [11]. Therefore there is a great interest in direct first-principle numerical simulations of strongly coupled degenerate systems which avoid such approximations. In this work we use the direct path integral Monte Carlo (DPIMC) method to calculate the thermodynamic properties of hydrogen and hydrogen - helium mixtures. This method is well established theoretically and allows the treatment of quantum and exchange effects without any preliminary physical approximations. Using the results of our simulation we compare them with the model based on the chemical picture [1, 2]. We also analyze the problem of plasma phase transition in dense hydrogen - helium mixtures and discuss several theoretical and experimental predictions of this phenomenon. ∗ Corresponding author: e-mail: filinov@ok.ru, Phone: +07 095 931 07 19, Fax: +07 095 485 79 90 c  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim