The Virial Expansion of the Hydrogen Equation of State in Comparison to <scp>PIMC</scp> Simulations: The Quasiparticle Concept, <scp>IPD</scp> , and Ionization Degree

ABSTRACT The properties of plasmas in the low‐density limit are described by virial expansions. Analytical expressions are known for the lowest virial coefficients from Green's function approaches. Recently, accurate path‐integral Monte Carlo (PIMC) simulations were performed for the hydrogen plasma at low densities by Filinov and Bonitz (Phys. Rev. E 2023 , 108 , 055212), which made a comparison of the virial expansions and the derivation of interpolation formulas possible. The exact expression for the second virial coefficient is used to test the accuracy of the PIMC simulations and the range of application of the virial expansions. To describe plasmas in a wider range of density and temperature, the concept of quasiparticles is considered. Medium modifications of free and bound states are obtained from the spectral function. Mean‐field effects are presented, such as exchange terms, Pauli blocking and screening. The density expansions of the quasiparticle shifts is considered. The combination of PIMC simulations with benchmarks from exact virial expansion results allows us to obtain precise results for the EoS in the low‐density range. At low densities, the results are compared with the Saha equation to introduce the medium‐dependent ionization potential. The relation to the Beth‐Uhlenbeck formula and concepts such as the Mott effect, ionization potential depression (IPD), and ionization degree are discussed. The limits of current PIMC results for hydrogen plasmas are shown. Further improvements of the PIMC simulations are required to compare with analytical benchmarks.