This paper analyzes nonequilibrium ionization problem by using multiple-time-scale perpurbation theory. The processes which are responsible for electron's average occupation probabilities Pn generally have much different time scales. In this paper the transitions between two neighbouring bound energy levels are considered as fast, the others, including the ionization processes, as slow. It is especially suitable for lower levels of high Z elements. The theory presented here gives analytic expressions for Pn as functions of ne, the number of free electrons. As a result, instead of solving equitions of dPn/dt we just need solving the differential equation for ne. So the problem is much simplified with avoiding the strong stiff which exists in equations dPn/dt. When radiation field reaches the Planck distribution, the Pn obtained here can naturally change into the Fermi-Dirac distribution.
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