Rate of Formation of Molecules by Radiative Association

A theoretical study is made of the rate at which free atoms form molecules by radiative association. Previous treatments of this problem are shown to be in error. A revised formula for the coefficient expressing the rate is derived. Approximate methods of evaluating this formula are discussed; and tables, designed to ease the computational labour, are presented. The methods developed are used to obtain the rate coefficients for $$CH,\,{CH}^{+}\,N_{2}^{+}\,\text{and}\,H_{2}^{+}$$ formation as these are of astrophysical or geophysical importance. In the case of $$H_{2}^{+}$$ the calculations can be performed with some precision. Free-free radiative collisions between H atoms and H⁺ ions are also investigated.