We present a new equation of state (EOS) for dense hydrogen/helium mixtures which covers a range of densities from $10^{-8}$ to $10^6$ g.cm$^{-3}$, pressures from $10^{-9}$ to $10^{13}$ GPa and temperatures from $10^{2}$ to $10^{8}$ K. The calculations combine the EOS of Saumon, Chabrier & vanHorn (1995) in the low density, low temperature molecular/atomic domain, the EOS of Chabrier & Potekhin (1998) in the high-density, high-temperature fully ionized domain, the limits of which differ for H and He, and ab initio quantum molecular dynamics (QMD) calculations in the intermediate density and temperature regime, characteristic of pressure dissociation and ionization. The EOS for the H/He mixture is based on the so-called additive volume law and thus does not take into account the interactions between the two species. A major improvement of the present calculations over existing ones is that we calculate the entropy over the entire density-temperature domain, a necessary quantity for stellar or planetary evolution calculations. The EOS results are compared with existing experimental data, namely Hugoniot shock experiments for pure H and He, and with first principle numerical simulations for both the single elements and the mixture. This new EOS covers a wide range of physical and astrophysical conditions, from jovian planets to solar-type stars, and recovers the existing relativistic EOS at very high densities, in the domains of white dwarfs and neutron stars.
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