Partition Functions and Mass Action Constants of Plasmas of Light Elements at Higher Temperatures

We first analyze the relations between the work of Planck and Klimontovich and show that Klimontovich's kinetic theory of non‐ideal plasmas confirms Planck's partition function for the hydrogen plasma. We discuss and check the Planck‐Brillouin‐Larkin (PBL) expressions for Hydrogen with PIMC calculations and derive new partition functions and mass action constants for Helium and Lithium. The new partition functions consider Planck's compensation effects between discrete and scattering states (Levinson effects). We show that any calculation of partition functions without taking compensation effects into account is quantum‐statistically incorrect. Our new expressions, which are given as series in β˜=$$ \tilde{\beta}= $$Ry/kBT$$ \mathrm{Ry}/{k}_{\mathrm{B}}T $$, are of particular interest for the temperature range beyond the ionization temperatures. There, the new partition functions disappear faster with temperature than the standard ones, which corresponds to a faster destruction of atoms in plasmas. The partition functions and the associated mass action constants are defined as the convergent contributions to the corresponding quantum‐statistical virial coefficients of pressure expansions. We estimate the third and fourth Coulomb virial coefficients and the mass action functions based on the new Slater functions. Based on the new results, which imply changes in the low orders of the parameter β˜$$ \tilde{\beta} $$, we predict lower concentrations for the formation of Hydrogen, Helium, and Lithium atoms and ions at higher temperatures than those obtained with standard methods.