Post-Threshold Energy Dependence of the Cross Section for Endoergic Processes: Vibrational Excitation and Reactive Scattering

The essential features of the translational energy dependence or excitation function σ(E_tr) for two types of endoergic collisional processes are deduced on the basis of information on the inverse, exoergic processes. Microreversibility is conveniently exploited via the symmetric yield function, Y(E), which is uniquely determined at a given total energy, E. In the case of the vibrational excitation of diatomic molecules by atomic or molecular impact $\mathrm{(T\; \to \; V)}$ , use is made of the abundant data on the temperature dependence of the $\mathrm{V\; \to \; T}$ relaxation time τ. The usual semiempirical two‐parameter representation of the relaxation process is transformed to yield an explicit functionality for the translational energy dependence of the inelastic excitation cross section ${\sigma }_{\text{0 → 1}}{\mathrm{(E}}_{\mathrm{tr}})$ , in the adiabatic region. For diatomics whose relaxation is slow (e.g., slow enough to be studied in a shock tube) the vibrational excitation cross section ${\sigma }_{\text{0 → 1}}$ is exponentially small in the post‐threshold region. These systems would be unsuitable for study by the crossed beam technique; the latter thus complements rather than replaces the more traditional relaxation methods. Also considered are endoergic chemical reactions whose inverse processes involve negligible activation barriers (e.g., ion—molecule reactions, reactive atom—molecule reactions, etc.). In all cases the dominant post‐threshold energy dependence of the reactive cross section σ_R(E_tr) for the endoergic process is fixed via the microreversibility constraint, so experimental data in this region do not provide as much information as is available from studies of the exoergic process. The deviation from a simple Arrhenius cross section functionality is determined by the long‐range final product interaction.