An equation of state for fully ionized hydrogen

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Abstract
We developed a model for the equation of state of fully ionized plasmas which we apply to hydrogen. Strong coupling effects between ions as well as finite temperature effects for the electron gas are taken into account. Two different models are considered corresponding respectively to weak and strong limits for the correlation effects between ions and electrons. The final equation of state covers the whole density and temperature domain characteristic of low-mass stars, main sequence stars, giant planets and inertially confined plasmas. An analytic expression for the electron gas compressibility sum rule and for the electronic screening length at finite temperature are derived, providing a link between the quantum Thomas Fermi and the classical Deby Hückel theories