H_2$]{}(J$_2$ $>$ 0).

This apparently null result deserves an explanation. We focus on equation (9) of @green75. This equation describes the different matrix elements that couple the various channels in the close-coupling equations. Some triangle rules apply which restrict the number of terms in the sum of equation (9); the relevant angular coupling algebra is represented there as a sum of terms of the type $$\label{eq:green75}
    \left(\begin{array}[c]{ccc} l &L'& L \\ 0 & 0 & 0
    \end{array}\right)
    \;
 \left(\begin{array}[c]{ccc} l_1 &J'_1& J_1 \\ 0 & 0 & 0
    \end{array}\right)
    \;
     \left(\begin{array}[c]{ccc} l_2 &J'_2& J_2 \\ 0 & 0 & 0
    \end{array}\right)
    \;
     \left\{\begin{array}[c]{ccc} L'& L & l \\ J_{12} & J'_{12} &
     J
    \end{array}\right\}\quad ,
$$ where we have the potential function expanded in terms of Eqs. (4) and (A2) in @green75, by means of the coefficients $v_{l_1l_2
l}$. The symbol $(\ldots)$ are 3-$j$ symbols, the $\{\ldots\}$ is a 6-$j$ symbol, see @messiah69. We also define $\vec{J}_{12}=\vec{J}_1+\vec{J}_2$. We have the following rules:

-   The para-[$\rm H_2$]{}inelastic collisions are dominated by the $J_2 = 0$ channel (the $J_2=2$ channel is closed till $E_{coll} \gtrsim 365.12
    \;\rm cm^{-1}$). Then, only the $l_2=0$ may be retained ($J_2=J'_2=0$), due to the third 3-$j$ symbol 