Recombination between electrons and atomic ions, I. Optically thin plasmas

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 $\alpha$ 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 plasmas which are optically thin. It is found that $\alpha$ 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$^\circ$K $\alpha$ 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$^\circ$K $\alpha$ 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 $\alpha$ 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 $\alpha$/Z is a function of a reduced temperature T/Z$^2$ and a reduced number density n(c)/Z$^7$ only. The values of the reduced coefficients are of comparable magnitude and have a similar dependence of the reduced temperature and density as the coefficients for hydrogen ion plasmas. The variation of the recombination coefficient $\alpha$ with Z in the same plasma (i.e. same n(c) and T) is investigated. It may be expressed in the form $\alpha \propto$ 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.