Problems in the use of statistical average atom potentials for estimating average degree of ionization

Consequences of a simple integral definition of electron charge bound to an ion are examined for Thomas-Fermi (TF) and Debye-Huckel-Thomas-Fermi (DHTF) average atom statistical potentials used to describe high temperature high density plasmas. A self-consistent scheme for calculating average degree of ionization within the DHTF approach is described. With the simple integral definition of bound charge the DHTF model, unlike the TF model, exhibits the anomalous behavior that degree of ionization can decrease as temperature increases. It is shown that this results from inclusion in the integration of electron charge density too extended and too near continuum energies to be physically considered as bound.