Transport‐collisional master equations for termolecular recombination as a function of gas density

Sets of transport‐collisional master equations are developed for the microscopic distribution n(R, E, L) of pairs over internal separation R, energy E, and orbital angular momentum L of (A–B) pairs in a background gas M of variable density. Expressions are also provided for the rate of recombination of A and B as a function of gas density in transport and collisional forms which, respectively, involve microscopic probabilities for association of dissociated (A–B) pairs and probabilities for collisional stabilization of bound pairs. Analytical solutions for the pair distributions n and microscopic probabilities for recombination are obtained in the classical absorption limit. They pertain to exact (A–B) trajectories under general symmetric interaction V(R) between A and B and are applied to ion–ion and electron–ion collisional recombination in a gas. A classical variational method is also presented. Useful expressions for the segments of hyperbolic and general trajectories enclosed by a sphere are derived in an Appendix.