as a function of the collision energy. For clarity, only the final CMSs $(0j00)$ have been shown. \[XSEL-ULE-1000-FIG\]](XSIN_H2-H2-allJ-vj1000-1nKto120K-rotdist.eps "fig:"){height="6cm"}

![ State-to-state cross sections for H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ collisions at an energy of 10$^{-3}$ K. The parameters corresponding to the black distributions are adopted in the final production calculations. Upper panel: convergence with respect to the angular anisotropic terms of the PES. Lower panel: convergence with respect to the number of points for the radial and angular integrations and the cut-off energy for the basis set. \[XS-STTOST-FIG\]](XS-ST2ST_H2-H2-vj1000-CONVERGENCE-fig1-1mK.eps "fig:"){height="6cm"}\
![ State-to-state cross sections for H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ collisions at an energy of 10$^{-3}$ K. The parameters corresponding to the black distributions are adopted in the final production calculations. Upper panel: convergence with respect to the angular anisotropic terms of the PES. Lower panel: convergence with respect to the number of points for the radial and angular integrations and the cut-off energy for the basis set. \[XS-STTOST-FIG\]](XS-ST2ST_H2-H2-vj1000-CONVERGENCE-fig2-1mK.eps "fig:"){height="6cm"}

In Fig. \[XS-STTOST-FIG\] we present the state-to-state rovibrational populations of the two molecules in H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ collisions at an energy of $E_c=10^{-3}$ K. Since rotational level resolved state-to-state cross sections are more difficult to converge compared to initial state-selected cross sections, we also include 