## Quantum, many-body, finite-temperature perturbation theory for an electron-ion system

The expansion in powers of the electron charge, e, for a neutral system of electrons (fermions) and ions (Maxwell-Boltzmann particles) is extended to order e{sup 4} for arbitrary values of temperature and density. The methods of calculation of the series terms will be illustrated, and some of the consequences of these results will be discussed. The ionization profile so derived, at least at high temperatures, will be contrasted with Saha theory. Some special features of hydrogen related to the possible plasma phase transition will be noted. (c) 2000 American Institute of Physics.