An Equation of State Model for Low-temperature Hydrogen and Its Isotopes

The low-temperature equations of state (EOS) of hydrogen and its isotopes are important to the design of high-energy-density (HED) experiments and improving the models of gas giants. In this presentation, I will discuss the development of a quantum statistical approach to model the EOS of solid hydrogen in various structures and across a broad range of pressures. This model explicitly considers the cold, vibration, and nuclear spin (coupled with molecular rotation in certain phases) contributions and combines first-principles calculations and quantum statistics to derive thermodynamically consistent EOS, including internal energy, Helmholtz free energy, entropy, and pressure as functions of temperature and density. The derived heat capacity, Hugoniot, and isentropes show good agreement with expectations based on previous low-pressure experiments. Finally, I will discuss the dependence of the results on nuclear spin states and masses, and connections to experiments aiming to reach the quantum metallic regime.