cross sections at a collision energy of $E_c=0.01$ eV. \[XSIN-THERMAL-1000-FIG\]](XS-ST2ST_H2-H2-vj1000-ANG-0.01eV.eps "fig:"){height="6cm"}

Figure \[XS-STTOST-FIG\] shows that vibrational relaxation of H$_2(v=1,j=0)$ by collisions with H$_2(v=0,j=0)$ is driven by high order anisotropic terms of the BMKP PES. Pogrebnya et al. [@Pogrebnya02] had previously investigated this issue and they had found that the high anisotropic terms of the BMKP PES lead to large values of the vibrational relaxation rate coefficients compared to experimental results. They found that a restricted version of this PES, referred to as the BMKPE PES which includes only $\lambda_1=\lambda_2=2$ components in Eq.  for the angular expansion of the interaction potential, yields better results in comparison with experimental data. In the upper panel of Fig. \[XSIN-THERMAL-1000-FIG\] we show the cross section for H$_2(v=1,j=0)$ + H$_2(v=0,j=0)$ $\to$ H$_2(v=0)$ + H$_2(v=0)$ collisions for $E_c = 0.001 - 1$ eV evaluated using the BMKPE (filled squares) and BMKP (filled circles) PESs. The corresponding results of Pogrebnya et al. [@Pogrebnya02] are also shown (open squares and circles) for comparison. While the results on the BMKPE PES are in overall good agreement, the results on the BMKP PES differ significantly at low collision energies (0.001 eV). The agreement improves with increase in collision energy and both 