within an angular momentum decoupling approximation called the coupled-states approximation (CSA). Lin et al. [@Lin02] used a time-dependent wave packet (TDWP) method and the CSA method to study pure rotational transitions in H$_2(v=0,j=0)$ + H$_2(v=0,j=0)$ collisions at thermal energies. Full-dimensional quantum studies without CSA have also been recently reported using the TDWP methods [@Gatti05; @Otto08; @Panda07]. Gatti et al. [@Gatti05] and Otto et al. [@Otto08] investigated para-para collisions involving H$_2(v=0,j=0)$ + H$_2(v=0,j=0)$, and Panda et al. [@Panda07] reported ortho-para collisions of H$_2(v=1,0,j=1)$ + H$_2(v=0,1,j=0)$. In a recent Communication [@Quemener08a], we reported rotational and vibrational relaxation of H$_2(v=1,j=0,2)$ in collisions with H$_2(v=0,j=0,2)$ at ultralow energies using the BMKP surface and a TIQM method that does not involve any angular momentum decoupling approximation. The calculations showed that indistinguishable molecule - molecule collisions may involve highly efficient near-resonant energy transfer if they are accompanied by simultaneous conservation of the total rotational angular momentum and internal energy of the molecules. This mechanism was found to be independent of the initial vibrational excitation of the molecules.

In this article, we present the full quantum dynamics of rovibrational energy transfer in para-H$_2$ + para-H$_2$ system from ultralow to high collision energies and compare our results with 