An example Partially ionized hydrogen plasma

The EOS of hydrogen in various physical conditions has been studied in many papers. Here we focus on the partially ionized atomic hydrogen at T > 3 x 104 K, that is relevant to neutron star atmospheres. Let us employ the chemical picture of the plasma. A detailed model in the framework of the chemical picture of a plasma consisting of protons, electrons, H atoms, and H2 molecules (in all quantum-mechanical states) was developed by Saumon et al. (1995). A completely analytic version of the associated free-energy model, applicable to the case of weakly degenerate electrons in the absence of molecules, was presented by Potekhin (1996b) and extended to the case of arbitrary electron degeneracy by Potekhin et al. (1999b). In this model,

is the sum of the ideal-gas free energies of electrons (2.49), protons (2.71), neutral species, and photons (thermal radiation), respectively, and

includes the contributions (2.87), (2.150), and (2.154) associated with interactions of protons and electrons, while Fexeu is responsible for interactions of neutral species with electrons, protons, and other neutral species.

The radiation term (which can be important only at low p or very high T) reads

where ctsb is the Stefan-Boltzmann constant.

The ideal-gas contribution of atoms reads

F1deu = kBT £ nk [in(nKAH/gK) — 1 — kabt] , (2.177)

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