that the density of states is quite small and the energy levels are sparsely spaced leading to small inelastic couplings. This is in contrast with the heavier alkali-metal systems with very high density of states, for which elastic scattering is less important than inelastic collisions at ultralow collision energies [@Quemener07]. In Fig. \[XSEL-ULE-1000-FIG\], the CMS (0800) is the most probable final state. This corresponds to a case where the vibrationally excited molecule H$_2(v=1,j=0)$ relaxes to the rotationally excited H$_2(v=0,j=8)$ state upon collisions with the ground state molecule H$_2(v=0,j=0)$. The final state distribution is determined by a compromise between conservation of the total internal energy and the rotational angular momenta of the colliding molecules.

![ Upper panel: Partial-wave resolved and total elastic cross sections for H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ collisions as a function of the collision energy. Lower panel: Inelastic state-to-state cross sections for the H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ system as a function of the collision energy. For clarity, only the final CMSs $(0j00)$ have been shown. \[XSEL-ULE-1000-FIG\]](XSEL_H2-H2-allJ-vj1000-1nKto120K-BW.eps "fig:"){height="6cm"}\
![ Upper panel: Partial-wave resolved and total elastic cross sections for H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ collisions as a function of the collision energy. Lower panel: Inelastic state-to-state cross sections for the H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ system 