On the foundation of the quantum statistics of thermal plasmas from Planck and Unsöld to recent developments

We study the basic results of quantum statistics of plasma in thermal equilibrium. First, we discuss the findings of early pioneers of quantum statistics of plasma, such as Max Planck, that the statistical thermodynamics of charged particles requires new concepts. We summarize the exact limiting results for low-density thermodynamics based on diagrammatic expansions and the concepts of Larkin–Matsubara–Kelbg and analyze hydrogen and helium plasmas. We discuss three relevant quantities that determine plasma thermodynamics: the atomic partition function, the equation of state (EOS), and the ionization potential depression. We provide improved virial expansions for the EOS that allow for an adequate description of the path integral Monte Carlo data up to intermediate densities. Taking into account existing controversies about the atomic partition function and the lowering of ionization energy, we show how the classical plasma theories of Planck and Unsöld can be integrated into modern quantum statistical methods. Typically, our partition functions disappear quickly at higher temperatures. This differs from many codes used for astrophysical and technical calculations; exceptions are the ACTEX and SAHA-S codes.