Perturbation theory calculation of the pressure for an electron–ion system

By means of finite-temperature, many-body perturbation theory we derive through order e4 the corrections to an ideal Fermi gas plus an ideal Maxwell–Boltzmann gas of ions. This computation is carried out for general values of the de Broglie density. The behavior of these coefficients is reported, and their implications for the ionization profile at low densities are described.