explained in the next section as well as $V_{a b}$. The total wave function is described as a sum of amplitudes of the rearrangement channels $(c=1-9)$ of Fig. 1 in the LS coupling scheme: $$\begin{aligned}
      \Psi_{JM}\!\!&(&\!\!^A_{\Lambda \Lambda}{\rm Z})
       =  \sum_{c=1}^{9} 
      \sum_{n,N,\nu}  \sum_{l,L,\lambda} 
       \sum_{S,\Sigma,I,K}
       C^{(c)}_{nlNL\nu\lambda S\Sigma IK} \nonumber  \\
      &  \times & {\cal A}_\Lambda{\cal S}_\alpha 
      \Bigg[  
       \Phi(\alpha) \left[\Phi_s(x)
    \; [ \chi_{\frac{1}{2}}(\Lambda_1) 
       \chi_{\frac{1}{2}}(\Lambda_2)
     ]_S \right]_\Sigma  \nonumber \\
  & \times  &    \left[ 
     [\: \phi^{(c)}_{nl}({\bf r}_c) 
         \psi^{(c)}_{NL}({\bf R}_c)
     ]_I \; \xi^{(c)}_{\nu\lambda} (\mbox{\boldmath $\rho$}_c) 
        \right]_{K}  \Bigg]_{JM}  \;  .
%(2.3)\end{aligned}$$

Here the operator ${\cal A}_{\Lambda}$ stands for antisymmetrization between the two $\Lambda$ particles, and ${\cal S}_{\alpha}$ is the symmetrization operator for exchange between $\alpha$ clusters when $x=\alpha$. $\chi_{\frac{1}{2}}(\Lambda_i)$ is the spin function of the $i$-th $\Lambda$ particle. Following the Jacobian-coordinate coupled-rearrangement-channel Gaussian-basis variational method of Refs. [@Kami88; @Kame89; @Hiyama95; @Hiya96; @Hiyama00; @Hiyama02; @Kamada01], we take the functional form of $\phi_{nlm}({\bf r})$, $\psi_{NLM}({\bf R})$ and $\xi^{(c)}_{\nu\lambda\mu} ({\boldmath \rho}_c)$ as $$\begin{aligned}
      \phi_{nlm}({\bf r})
      &=&
      r^l \, e^{-(r/r_n)^2} 
       Y_{lm}({\widehat {\bf r}})  \;  ,
 \nonumber \\
      \psi_{NLM}({\bf R})
      &=&
       R^L \, e^{-(R/R_N)^2} 
       Y_{LM}({\widehat {\bf R}})  \;  ,
 \nonumber \\
      \xi_{\nu\lambda\mu}(\mbox{\boldmath $\rho$})
      &=&
       \rho^\lambda \, e^{-(\rho/\rho_\nu)^2} 
       Y_{\lambda\mu}({\widehat {\mbox{\boldmath $\rho$}}})  \; ,
%(2.4)\end{aligned}$$ where the Gaussian range parameters are chosen to lie 