Rate constants for the H⁺ + H₂ reaction from 5 K to 3000 K with a statistical quantum method

An exhaustive investigation of state-to-state H⁺ + H₂(v, j) → H⁺ + H₂(v', j') transitions for rovibrational levels of molecular hydrogen below 1.3 eV from the bottom of the H₂ well is carried out by means of a statistical quantum method, which assumes the complex-forming nature of the process. Integral cross sections for transitions involving states H₂(v = 0, j = 0-12), H₂(v = 1, j = 0-8), and H₂(v = 2, j = 0-3) are obtained for collision energies within a range of E_min = 10^-5 eV and E_max = 2 eV. Rate constants are then calculated between T = 5 K and 3000 K, and they are compared, when possible, with previous values reported in the literature. As a first application, the cooling rate coefficient of H₂ excited by protons is determined and compared with a recent estimate.