momentum $L_i$ from the terms of degree $L_i$, we may replace the term $\left(\rho_{ij}{{\mbox{\boldmath $e$}}}_i\cdot{{\mbox{\boldmath $e$}}}_j\right)^{n_{ij}}$ with just one piece $$\frac{ (-\rho_{ij})^{n_{ij}} n_{ij}! \sqrt{2n_{ij}+1}}{B_{n_{ij}}}
\left[Y_{n_{ij}}({{\mbox{\boldmath $e$}}}_i)Y_{n_{ij}}({{\mbox{\boldmath $e$}}}_j)\right]_{00}.$$ Other pieces like $\left[Y_{\kappa}({{\mbox{\boldmath $e$}}}_i)Y_{\kappa}({{\mbox{\boldmath $e$}}}_j)\right]_{00}$ with $\kappa < n_{ij}$ do not contribute to the matrix element. We thus have a product of 15 terms of $\left[Y_{n_{ij}}({{\mbox{\boldmath $e$}}}_i)Y_{n_{ij}}({{\mbox{\boldmath $e$}}}_j)\right]_{00}$. The coupling of these terms is done by defining various coefficients that are all expressed in terms of Clebsch-Gordan, Racah, and 9$j$ coefficients. For example, we make use of the formulas $$\begin{aligned}
& &{\hspace{-1cm}}[Y_a({{\mbox{\boldmath $e$}}}_1)Y_a({{\mbox{\boldmath $e$}}}_2)]_{00}\ [Y_b({{\mbox{\boldmath $e$}}}_1)Y_b({{\mbox{\boldmath $e$}}}_3)]_{00}\ 
[Y_c({{\mbox{\boldmath $e$}}}_2)Y_c({{\mbox{\boldmath $e$}}}_3)]_{00}
\nonumber \\
& \to& X(abc)\ [[Y_{a+b}({{\mbox{\boldmath $e$}}}_1)Y_{a+c}({{\mbox{\boldmath $e$}}}_2)]_{b+c}Y_{b+c}({{\mbox{\boldmath $e$}}}_3)]_{00},\\
\nonumber\\
& &{\hspace{-1cm}}[Y_a({{\mbox{\boldmath $e$}}}_1)Y_a({{\mbox{\boldmath $e$}}}_4)]_{00}\ [Y_b({{\mbox{\boldmath $e$}}}_1)Y_b({{\mbox{\boldmath $e$}}}_5)]_{00}\ 
[Y_c({{\mbox{\boldmath $e$}}}_1)Y_c({{\mbox{\boldmath $e$}}}_6)]_{00}
\nonumber \\
&\to& R_3(abc)\ [Y_{a+b+c}({{\mbox{\boldmath $e$}}}_1)\ [[Y_{a}({{\mbox{\boldmath $e$}}}_4)Y_{b}({{\mbox{\boldmath $e$}}}_5)]_{a+b}Y_c({{\mbox{\boldmath $e$}}}_6)]_{a+b+c}]_{00}.\end{aligned}$$ Here the symbol $\to$ indicates that no other terms arising from the left hand side of the equation contribute to the integration over the angles ${{\mbox{\boldmath $e$}}}_i$s, so that only the term on the right hand side has to be retained. Another coefficient is $$\begin{aligned}
&&{\hspace{-1cm}}[[[Y_a({{\mbox{\boldmath $e$}}}_4)Y_b({{\mbox{\boldmath $e$}}}_5)]_qY_c({{\mbox{\boldmath $e$}}}_6)]_Q\ 
[[Y_{a'}({{\mbox{\boldmath $e$}}}_4)Y_{b'}({{\mbox{\boldmath $e$}}}_5)]_{q'}Y_{c'}({{\mbox{\boldmath $e$}}}_6)]_{Q'}]_{\ell}
\nonumber \\
&\to& \sum_{\ell'}W(abcqQ,a'b'c'q'Q',\ell \ell')
[[Y_{a+a'}({{\mbox{\boldmath $e$}}}_4)Y_{b+b'}({{\mbox{\boldmath $e$}}}_5)]_{\ell'}Y_{c+c'}({{\mbox{\boldmath $e$}}}_6)]_{\ell}.\end{aligned}$$ Expressions for the coefficients, $X, R_3, W$, are given in 