Transition probabilities and differential cross sections for vibrational excitation in collisions of H+ with H2, HD, and D2

The angle and energy dependence of the differential cross sections are reported for resolved vibrational transitions in low-energy collisions of H⁺ with H₂, HD, and D₂. The specific transition probabilities for the different isotopic molecules scale in the order D₂ > HD > H₂ at the same initial kinetic energy and scattering angle, but when compared at the same reduced kinetic energy, Eᵣ=E/ℏω, are approximately equal, suggesting that the interaction leading to vibrational excitation in this system is primarily the dilution of the molecular bond as the proton passes. We discuss the results in terms of a semiclassical model for vibrational excitation based on an oscillator driven by a time-dependent force.