tokens: in determining the fractional abundance of atomic hydrogen in dark clouds. The main results are listed below. (i) The CR dissociation rate, ζ diss , is primarily determined by secondary electrons produced during the primary CR ionisation process. These secondary electrons can efficiently dissociate H 2 and represent the only source of atomic hydrogen at column densities higher than ≈10 21 cm −2 , regulating the ratio in dark clouds. (ii) ζ diss entering the balance Eq. ( 4 ) is not equal to the ionisation rate ζ ion , as assumed in some previous work. We find that the ratio ζ diss ∕ ζ ion varies between ≈0.63 and ≈0.7, depending on the column density range, while ζ ion is a decreasing function of the column density. (iii) Even given the uncertainties in the values of H 2 formation rate, temperature, total hydrogen volume density, and IS UV radiation field for each cloud, only a CR proton spectrum enhanced at low energies (such as our model ) is capable of reproducing the upper values of measured f H under the assumption of steady state. We note that neither model nor model is able toreproduce the entire set of observational data: the spread in the values of f H at any given column density must be attributed to time dependence or to individual characteristics of each cloud. For example, tangled magnetic field lines and/or higher volume densities would result in a stronger CR attenuation and thereforein a lower f H . (iv) An accurate description of H 2 dissociation in dense environments is essential because many chemical processes (such as CO hydrogenation and its depletion degree onto dust grains, or formation of complex organic molecules) critically depend on the abundance of atomic hydrogen. Appendix A Equilibrium distribution of protons and H<sub>fast</sub> atoms at low energies Because of the process of electron capture at low energies, CR protons interacting with H 2 are efficiently neutralised, creating fast H atoms. In parentheses we list the cross section of the respective process. At the same time, H fast atoms reacting with H 2 yield The electron capture by protons, reaction ( A.1 ), and the reaction of H fast self-ionisation, reaction ( A.3 ), are catastrophic processes, since the respective projectile particles disappear after such collisions. The reactions of H 2 ionisation and dissociation by H fast atoms, reactions ( A.2 ) and ( A.4 ), respectively, are continuous loss processes, where the projectile kinetic energy decreases only slightly after each collision. The efficiency of continuous energy losses is generally characterised by the projectile stopping range (see, e.g. Padovani et al. 2009 ). For our calculations, is taken from Rudd et al. (1983) , is adopted from Phelps (1990) and Kunc Soon (1991) , is computed by Stier Barnett (1956) , van Zyl et al. (1981) , and Phelps (1990) , and is taken from Dove Mandy (1986) and Esposito Capitelli (2009) . In Fig. A.1 , we plot the cross sections and the inverse of the proton
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