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On the Theory of Recombination

On the theory of recombination
Authors: George Jaffé;

On the Theory of Recombination

Abstract

In Section I a general formula for $\ensuremath{\alpha}$, the coefficient of recombination of ions in gases, is developed. It covers all ranges of pressures and temperatures and can be made to include all types of recombination (preferential, initial and volume ionization). The evaluation of the general formula, (1.1), depends on the relative values of three linear quantities: the mean free path of the ions $\ensuremath{\lambda}$, the mean distance between ions of different signs $\overline{r}$ and the well-known parameter ${a}_{0}=\frac{{e}^{2}}{(\mathrm{kKT})}$. In Section II the case $\ensuremath{\lambda}\ensuremath{\ll}{a}_{0}$ is treated. The mechanism of recombination then depends on the ratio $\frac{{a}_{0}}{\overline{r}}$. If $\frac{{a}_{0}}{\overline{r}}$ is large the migration of the ions under their mutual attraction prevails and (1.1) leads to Langevin's formula; in the opposite case, $\frac{{a}_{0}}{\overline{r}}\ensuremath{\ll}1$, diffusion is the decisive feature and 1.1 leads to a formula which is practically identical with that of Harper. In Section III the case $\ensuremath{\lambda}\ensuremath{\gg}{a}_{0}$ is treated by a method previously developed by the author. Under certain restrictions (1.1) reduces to Thomson's formula, but in general $\ensuremath{\alpha}$ depends on the concentration of the ions. In Section IV it is shown that (1.1) is in fair agreement with such experimental data as are available for the region of transition between the cases treated in Sections II and III.

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Theory of the electron

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
45
Top 10%
Top 10%
Average
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