The usual approach to the problem of the Equations Of State (EOS) for White Dwarfs and super giant Planets, under the conditions of high densities and low temperatures, faces two problems.

The first has to do with Pressure Ionization : the energy levels of the electrons in the case of extreme pressure ionization cannot be treated in the same way as the energy levels in a single isolated atom. The simple treatment of pressure ionization, in which the level of the continuum is reduced by an amount equal to the electrostatic energy, leads to problem because the number of energy levels, entering the Saha equation (partition functions), is not conserved, also the usual approach may lead to absurd results in which ions recombine as the density increases.