The practice of surprisal inference: products' state distribution in the chemiluminescent-molecule reaction of C⁺ + H₂

State-of-the-art information-theoretic procedures are illustrated by a practical application to the problem of the products' rotational and vibrational state distributions for the ion-molecule reactions C⁺ + H₂, D₂ → CH⁺, CD⁺(A ¹Π) + H, D. The analysis shows that to within the experimental uncertainty the rotational energy distributions (same for both isotopic products) can be characterized by single-constraint surprisals whose (positive) parameter θ_R increases with (total) energy E. The vibrational state distributions at low E are essentially the unconstrated "prior" distributions; at higher E the vibrational surprisal parameter λ_ν (same for both isotopic products) becomes increasingly negative, as the reaction dynamics change from "complex-mode" to "direct-mode", with concomitant vibrational population inversion. Simple dynamical consideration which account for the isotopic invariance (in the reduced variables) are noted. An appendix notes that surprisal inference, utilizing the maximal entropy principle, provides an optimal functional form for a "trial" population distribution with a minimum number of adjustable parameters which is suitable for use in fitting spectral intensities.