The hydrogen plasma is studied at temperatures T similar to 10(4)-10(6
) K using the free energy minimization method. A simple analytic free
energy model is proposed which is accurate at densities rho less than
or similar to 1 cm(-3) and yields the convergent internal partition fu
nction of atoms. The occupation probability formalism is modified for
solving the ionization equilibrium problem. The ionization degree and
equation of state are calculated and compared with the results of othe
r models. (C) 1996 American Institute of Physics.