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We perform a pure quantum-mechanical calculation for the non-reactive scattering in atomic and molecular hydrogen-hydrogen collisions, i.e. H 2 +H 2  and H+H 2 . Different potential energy surfaces (PESs) for the H 3  and H 4  atomic systems have been used. The rigid rotor model of the diatomic molecules, i.e. when the distance between hydrogen atoms is fixed at some average equilibrium value, has been applied in our calculation. After this preparatory stage the astrophysical H 2 -cooling function can be estimated at different astrophysical conditions and temperatures.

Rotational Energy Transfer Non-Reactive Hydrogen-Hydrogen Collisions at Low Temperatures of Astrophysical Interest