Cosmic-ray excitation and ionisation rates. Upper panel: CR excitation rate due to secondary electrons as a function of H₂ column density for the H₂ rovibrational transitions (v, J) = (0, 0) → (1, 0) and (v, J) = (0, 0) → (1, 2) (solid and dashed lines, respectively). Black and red lines show the rates due to secondaries produced by CR protons, , and primary CR electrons, , respectively. Lower panel: CR ionisation rate due to CR protons (solid black lines) and CR electrons (solid red line). All the curves include the contribution to ionisation due to the corresponding generation of secondary electrons. Labels on the left in both panels denote the low-energy spectral slope (parameter α in Eq. (2)). The cases α = 0.1 and α = −0.8 correspond to models and , respectively.