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.