Cold and ultracold H$_2$-H$_2$ collisions on high accuracy ab initio potentials*

We report quantum calculations of rovibrational transitions in H$_2$ + H$_2$ collisions on different ab initio potential surfaces (PESs). The PESs employed include the six-dimensional interaction potential of Hinde [1] and a hybrid potential constructed from the Hinde potential and the high accuracy 4-dimensional PES of Patkowski et al. [2]. Results show that vibrational relaxation cross sections are sensitive to details of the potentials at low energies but the sensitivity is significantly suppressed for quasiresonant transitions that involve small energy gaps and that conserve the total rotational angular momentum of the colliding molecules. Additionally, we present results for H$_2(v=2)$ + H$_2(v = 0)$ collisions and explore competition between vibration-vibration (VV) transfer leading to H$_2(v=1)$ +H$_2(v=1)$ products and vibration-translation (VT) transfer yielding H$_2(v=1)$ + H$_2(v=0)$ products. Results show that the VV process dominates over the VT process, in agreement with available experimental data. [1] Robert J. Hinde, J. Chem. Phys. {\bf 128}, 154308 (2008). [2] K. Patkowski, W. Cencek, P.Jankowski, K. Szalewicz, J. B. Mehl, G. Garberoglio, and A. H. Harvey, J. Chem. Phys. {\bf 129}, 094304 (2008).