Results for quantum mechanical calculations of the integral cross sections and corresponding thermal rate coefficients for para-/ortho-H2+HD collisions are presented. Because of significant astrophysical interest in regard to the cooling of primodial gas the low temperature limit of para-/ortho-H2+HD is investigated. Sharp resonances in the rotational state-resolved cross sections have been calculated at low energies. These resonances are important and significantly contribute to the corresponding rotational state-resolved thermal rate coefficients, particularly at low temperatures, that is less than $T sim 100$K. Additionally in this work, the cross sections for the elastic HD+HD collision have also been calculated. We obtained quite satisfactory agreement with the results of other theoretical works and experiments.
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