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Example: triple electron-ion recombination and stepwise ionization for K

The rate coefficients of triple electron-ion recombination and stepwise ionization for K are evaluated within the framework of the simplified model that is based on assumption that the most slow stage of the recombination process is the three-body collisional capture of a free electron onto one of the highly excited states of an atom. The binding energy of such a state is of an order of the electron temperature, which is supposed to be much less that the ionization potential of the atomic particle. In such conditions the distribution of electrons over the excited states is close to the equilibrium, Boltzmann one, for which reason the recombination rate constant does not depend on the electron number density and is expressed through the  rate constant of the electron capture. The above-described mechanism governs the opposite process which is the step-wise electron impact ionization of atomic particles in plasma. The process proceeds at a nearly equilibrium distribution of weakly bound electrons over excited states of an atomic particle. The relation for the step-wise ionization rate constant is expressed through that for electron-ion recombination using the detailed balance principle.

Results of calculation is presented in figure. It is seen that the simplified approach applied provides quite good agreement with data obtained on the basis of comprehensive state-to-state calculation using the set of electron impact inelastic collision cross sections found within the frame of Born approximation.

The results of calculations of rate constant of the process K(+) + e + e => K + e (krec) and reversed process K + e => K(+) +e (kst). Points show the results of comprehensive state-to-state calculation of the recombination rate performed by D.R.Bates, A.E.Kingstone and McWhirter, Proc. Roy. Soc. A267 297 (1962)

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