Y_{l}^{m}(\Omega')\end{aligned}$$ and note that the integration of three spherical harmonics yields $3j$ symbols [@Brink:104381]:

$$\begin{aligned}
    \int Y_{l_{1}}^{m_{1}}(\Omega) Y_{l_{2}}^{m_{2}}(\Omega)
    Y_{l_{3}}^{m_{3}}(\Omega) d\Omega =
    \sqrt{\frac{(2l_1+1)(2l_2+1)(2l_3+1)}{4 \pi}}
    \begin{pmatrix}
      l_1 & l_2 & l_3
      \\
      0 & 0 & 0
    \end{pmatrix}
              \begin{pmatrix}
                l_1 & l_2 & l_3
                \\
                m_1 & m_2 & m_3
              \end{pmatrix}. \label{eq:34}
  \end{aligned}$$

This allows us to split the result into the radial and angular parts as $$\begin{aligned}
    B_{\nu_2,\nu_4}^{\nu_1,\nu_3} =
    -\delta_{m_{j2}-m_{j1}}^{m_{j3}-m_{j4}} (-1)^{2
    m_{j1}-m_{j2}-m_{j3}} \sum_p \left( \Phi_{\nu_1,\nu_2}^p \otimes
    \Phi_{\nu_3,\nu_4}^p \right) \cdot
    \sigma_{\nu_1,\nu_2,\nu_3,\nu_4}^p, \label{eq:35}
  \end{aligned}$$ with the angular part given by $$\begin{aligned}
    \Phi_{\nu_1,\nu_2}^p = \left(
    \begin{array}{c}
      \begin{pmatrix}
        \kappa_1 & \kappa_2 & p
        \\
        0 & 0 & 0
      \end{pmatrix}
                \left(
                \phi_{\kappa_1,m_{j1} -
                \frac{1}{2}}^{\kappa_2,m_{j2}-\frac{1}{2}}
                (p) -
                \phi_{\kappa_1,\frac{1}{2} -
                m_{j1}}^{\kappa_2,\frac{1}{2}-m_{j2}}
                (p)\right)
      \\
      \begin{pmatrix}
        -\kappa_1 & -\kappa_2 & p
        \\ 0 & 0 & 0
      \end{pmatrix}
      \left(\phi_{-\kappa_1,m_{j1} -
                   \frac{1}{2}}^{-\kappa_2,m_{j2}-\frac{1}{2}}(p) -
                   \phi_{-\kappa_1,\frac{1}{2} -
                   m_{j1}}^{-\kappa_2,\frac{1}{2}-m_{j2}}(p)\right)
    \end{array}\right), \label{eq:36}
  \end{aligned}$$ where $$\begin{aligned}
    \phi_{k_1,m_1}^{k_2,m_2}(p) = \sqrt{(k_1-m_1)(k_2-m_2)}
    \begin{pmatrix}
      \kappa_1 & \kappa_2 & p
      \\
      -m_{1} & m_{2} & m_{1}-m_{2}
    \end{pmatrix}. \label{eq:37}
  \end{aligned}$$

Furthermore, the radial part is given by $$\begin{aligned}
    \sigma_{\nu_1,\nu_2,\nu_3,\nu_4}^p = \int
    {{G_{\nu_1}^{*}(r)G_{\nu_2}(r)}\choose{F_{\nu_1}^{*}(r) F_{\nu_2}(r)}}
    \otimes
    {{G_{\nu_3}^{*}(r')G_{\nu_4}(r')}\choose{F_{\nu_3}^{*}(r') F_{\nu_4}(r')}}
    \frac{r_<^p}{r_>^{p+1}}drdr', \label{eq:38}
  \end{aligned}$$ where the dependence on $Z^*$ has been omitted for clarity. Eq. (\[eq:38\]) can be calculated analytically by noting that the integral of 