We consider collisional excitation of H molecules in C-type shocks propagating in dense molecular clouds. New data on collisional rate coefficients for (de-)excitation of H molecule in collisions with H atoms and new H dissociation rates are used. The new H-H collisional data are state of the art and are based on the most accurate H potential energy surface. We re-examine the excitation of rotational levels of H molecule, the para-to-ortho-H conversion, and H dissociation by H-H collisions. At cosmic ray ionization rates s and at moderate shock speeds, the H/H ratio at the shock front is mainly determined by the cosmic ray ionization rate. The H-H collisions play the main role in the para-to-ortho-H conversion and, at s, in the excitation of vibrationally excited states of H molecule in the shock. The H ortho-to-para ratio (OPR) of the shocked gas and column densities of rotational levels of vibrationally excited states of H are found to depend strongly on the cosmic ray ionization rate. We discuss the applicability of the presented results to interpretation of observations of H emission in supernova remnants.

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