The broadening of the electronic energy levels of atoms and ions in hot and dense plasmas is taken to be an energy band with a Gaussian distribution of the density of states, which is normalized to ensure that the integration of the density of state over one band is equal to the statistical weight of the corresponding atomic level. The distribution of the bound electrons among the energy bands is determined by the continuum Fermi-Dirac distribution. Within a self-consistent field average atom approach, it has been shown that explicit considerations for the electronic energy level broadening have significant effects on the ionization of the atoms in hot and dense plasmas. The instability of the pressure induced electronic ionization with density, which occurs often in a normal average atom model and is avoided usually by introducing pseudoshape resonance states, disappears naturally. As examples, the density dependence of the average ionization of Al and Au at 1, 10, 100, and 1000eV are presented.
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