\[XS-EL-FIG\] for collision energies up to 0.03 eV. The theoretical results of Lee et al. [@Lee06] and experimental results of Bauer et al. [@Bauer76] are also included for comparison. The present results do not differ significantly from the results of Lee et al. The full calculation predicts slightly larger values for the elastic cross section compared to the rigid rotor results. Overall, the DJ PES predicts results in better agreement with the experimental results.

![ (Color online) Elastic cross section for H$_2(v=0,j=0)$ + H$_2(v=0,j=0)$ collisions as a function of the incident collision energy. The experimental results of Bauer et al. [@Bauer76] and theoretical results of Lee et al. [@Lee06] are also shown. \[XS-EL-FIG\]](XSEL_H2-H2-allJ-vj0000-0.005eVto0.03eV.eps){height="12cm" width="8cm"}

![ State-to-state cross sections for rotational excitation in H$_2(v=0,j=0)$ + H$_2(v=0,j=0)$ collisions as functions of the collision energy. The results of Otto et al. [@Otto08] are included for comparison. \[ST2STXS-THERMAL-0000-FIG\]](XSELIN_H2-H2-la8lb8-v0j8-allJ-vj0000-0eVto1.2eV-BW-FULL-SBS-andRR.eps){height="12cm" width="8cm"}

A number of recent studies have reported rotational excitation cross sections in collisions between two rovibrationally ground state H$_2$ molecules [@Gatti05; @Lee06; @Otto08]. The studies of Gatti et al. [@Gatti05] and Otto et al. [@Otto08] employed the full-dimensional multiconfiguration time-dependent Hartree (MCTDH) approach while that of Lee et al. [@Lee06] employed the TIQM approach within 