Recombination of electron–ion pairs for arbitrary mean free path

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Abstract
A theory is developed of the dependence of the steady-state electron–ion pair recombination rate constant on the electron mean free path. The problem, in classical mechanics, is reduced to the stochastic dynamics of the electron in the one-dimensional effective potential Ṽ(R)=−kTRc/R −2kT ln R. Rc is the Onsager length Ze2/4πεkT. For a large mean free path λ, the recombination rate is determined by energy relaxation of electrons which cross the transition state of Ṽ(R) at RT=Rc/2, whereas for small λ the Debye result for spatial diffusion-controlled recombination is obtained. The theory gives the dependence of the rate in the crossover regime where λ is comparable to Rc. The results are in good agreement with experiment and Monte Carlo simulations.