Eur. Phys. J. Special Topics 229, 3403–3431 (2020)
https://doi.org/10.1140/epjst/e2020-000066-6

Review

Hydrogen, helium and lithium plasmas at high pressures^★

¹ Institute of Physics, Humboldt University, 10117 Berlin, Germany
² Institute of Physics, Rostock University, 18059 Rostock, Germany
³ National Research Nuclear University (MEPhI), 115409 Moscow, Russia

^a e-mail: heidi.reinholz@uni-rostock.de

Received: 14 April 2020
Accepted: 5 November 2020
Published online: 21 December 2020

Abstract

The equations of state (EoS) and other thermodynamic properties of plasmas of the light elements H, He, and Li, are calculated using inverted fugacity expansions. Fugacity expansions are known as an alternative to density expansions but show often an inferior convergence. If, however, the inversion can be solved, the fugacity representations may be very efficient. In particular, the contributions of deeply bound states are included in the fugacity expansion in a very effective way. The mathematical problems on nonlinearity connected with the inversion of fugacities to densities are reduced to solvable algebraic problems. The inversion of fugacities to densities is solved separately for two density regions: (i) In the low density, non-degenerate region we consider ring contributions describing screening effects and ladder contributions describing bound state formation. (ii) In the high density, degenerate region the electrons are described by the Fermi–Dirac distribution. Hartree–Fock contributions and Pauli blocking have to be taken into account. The ions are considered as classical, strongly correlated subsystem eventually forming a Wigner lattice. We solve the inversion problem for each of the regions. Near the crossing point, the separate solutions are connected to each other, either by smooth concatenation at the crossing point or by Padé approximations.