## Abstract

Consideration is given to the interacting collisional and radiative processes occurring in a plasma. A statistical theory describing the general loss mechanism, for which the name *collisional-radiative recombination* is proposed, is described. This theory enables the collisional-radiative recombination coefficient a to be determined knowing the relevant spontaneous transition probabilities and the rate coefficients for radiative recombination and collisional excitation and ionization. Detailed calculations are carried out on hydrogen-ion plasm as which are optically thin. It is found that α is an increasing function of the number density of free electron *n(c)* the increase being especially marked if the electron temperature *T* is low; for example, if *T* is 250 °K α becomes almost 20 times as great as the radiative recombination coefficient (which describes the loss in a very tenuous plasma) when *n(c)* is only about 10^{8}/cm^{3}, whereas if *T* is 64 000°K a does not become as great as this until *n(c)* is about 10^{18}/cm^{3}. From a similar investigation in which the ground level of the hydrogen atom is made inaccessible (in crude representation of an alkali atom) it is inferred that the value of a is probably not very sensitive to the species of singly charged ion involved. Recombination of electrons with bare nuclei of charge *Ze* to form hydrogenic ions is similarly treated for an optically thin plasma. It is shown that to a close approximation the reduced coefficient α/*Z* is a function of a reduced tem perature *T/Z*^{2} and a reduced number density *n(c)/Z*^{7} only. The values of the reduced coefficients are of com parable m agnitude and have a similar dependence of the reduced temperature and density as the coefficients for hydrogen ion plasmas. The variation of the recombination coefficient α with *Z* in the same plasma (i.e. same *n(c)* and *T*) is investigated. It may be expressed in the form a α ∝ *Z*^{z} where the index z depends on *n(c)* and *T*. Though z is generally positive as would be expected, it is negative if *n(c)* and *T* are very high. A physical explanation of this is presented.

## Footnotes

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- Received October 23, 1961.

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