We present a rigorous study of vibrational relaxation in p-H2 + p-H2collisions at cold and ultracold temperatures and identify an efficientmechanism of ro-vibrational energy transfer. If the colliding molecules are indifferent rotational and vibrational levels, the internal energy may betransferred between the molecules through an extremely state-selective processinvolving simultaneous conservation of internal energy and total rotationalangular momentum. The same transition in collisions of distinguishablemolecules corresponds to the rotational energy transfer from one vibrationalstate of the colliding molecules to another.
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