Elastic and inelastic cross sections for H$_2(v=0,j=2)$ + H$_2(v=0,j=0)$ collisions. Lower panel: Elastic and inelastic cross sections for H$_2(v=0,j=2)$ + H$_2(v=0,j=2)$ collisions. \[XSEL-ULE-0000-0200-0202-FIG\]](XSELIN_H2-H2-allJ-vj0202-1nKto120K.eps "fig:"){height="5.5cm"}

In Fig. \[XSEL-ULE-0000-0200-0202-FIG\] we show cross sections for H$_2(v=0,j=0)$ + H$_2(v=0,j=0)$ (upper panel), H$_2(v=0,j=2)$ + H$_2(v=0,j=0)$ (middle panel) and H$_2(v=0,j=2)$ + H$_2(v=0,j=2)$ (lower panel) collisions on the BMKP PES. Previous results of Lee et al. [@Lee06] on the BMKP and DJ PESs and Forrey [@Forrey01] on the ZR PES based on the rigid rotor model are also shown for comparison. The results on the BMKP PES in the upper panel show that the rigid rotor approximation is reliable in predicting elastic cross sections for collisions between two ground state H$_2$ molecules. The DJ potential predicts similar results as the BMKP potential except for the slight shift in the location of the resonance at about $E_c=2$ K. The agreement between the DJ and BMKP results is excellent for collision energies above 4 K. Overall, the elastic cross section appears to be less sensitive to the choice of the PES and the dynamics approximation. In the middle panel of Fig. \[XSEL-ULE-0000-0200-0202-FIG\] we show the elastic and inelastic rotational de-excitation cross sections for H$_2(v=0,j=2)$ + H$_2(v=0,j=0)$ collisions. As in 