Ultracold collisions between two light indistinguishable diatomic molecules: elastic and rotational energy transfer in HD+HD

A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T\sim {10}^{-8}$ K. A global six-dimensional H${}_2$-H${}_2$ potential energy surface is adopted from a previous work [Boothroyd {\it et al.}, J. Chem. Phys., {\bf 116}, 666 (2002).] State-resolved integral cross sections ${\sigma }_{ij\to i^{\mathrm{\prime }}{j}^{\mathrm{\prime }}}({\epsilon }_{kin})$ of different quantum-mechanical rotational transitions $ij\to i^{\mathrm{\prime }}{j}^{\mathrm{\prime }}$ in the HD molecules and corresponding state-resolved thermal rate coefficients $k_{ij\to i^{\mathrm{\prime }}{j}^{\mathrm{\prime }}}(T)$ have been computed. Additionally, for comparison, H${}_2$+H${}_2$ calculations for a few selected rotational transitions have also been performed. The hydrogen and deuterated hydrogen molecules are treated as rigid rotors in this work. A pronounced isotope effect is identified in the cross sections of these collisions at low and ultracold temperatures.