|A\_3\^[++]{}&=&\^+\^+,\
|A\_4\^[++]{}&=&(\^[++]{}\_r\^0 -\^[++]{}\_i\^0)/ ,\
|A\_5\^[++]{}&=&\^+\^+,\
|A\_6\^[++]{}&=&(\^[++]{}\_r\^0 +\^[++]{}\_i\^0)/ ,\
|A\_7\^[++]{}&=&(\^+\^+ +\^[++]{}\_r\^0)/ ,\
|A\_8\^[++]{}&=&(\^+\^+ +\^+\^+ +\^[++]{}\_r\^0)/ ,\
|A\_9\^[++]{}&=&(\^+\^+ -\^+\^+ -\^[++]{}\_i\^0)/ ,\
|A\_[10]{}\^[++]{}&=&(\^+\^+ +\^+\^+ -2\^[++]{}\_r\^0)/ ,\
|A\_[11]{}\^[++]{}&=&(\^+\^+ - \^+\^+ +2\^[++]{}\_i\^0)/ . The corresponding doubly-charged two-body states with the charge $-2$ can be obtained by $C$ transformation in the above states with the charge $+2$.\
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There are three triply-charged states with the electric charge $+3$, and the subset of the transition matrix for the initial and final states can be diagonalized by the following eigenstates as |A\_1\^[+++]{}&=&\^[++]{}\^+,\
|A\_2\^[+++]{}&=&\^[++]{}\^+,\
|A\_3\^[+++]{}&=&\^[++]{}\^+. All the eigenstates with the opposite electric charge can be obtained by the $C$ transformation of these eigenstates with the charge $+3$.\
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Finally, we have only one quadruply-charged state for each electric charge of $+4$ and $-4$, |A\_1\^[++++]{}&=&\^[++]{}\^[++]{},\
|A\_1\^[—-]{}&=&\^[–]{}\^[–]{}.

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In summary, the transition matrix $T$ has been block-diagonalized as T = , \[Tmatrix\] where block-diagonal transition submatrices for the neutral, the singly-charged, the doubly-charged, the triply-charged, and the quadruply-charged two-body states, $T^0$, $T^\pm$, $T^{\pm\pm}$, $T^{\pm\pm\pm}$, and $T^{\pm\pm\pm\pm}$, respectively, are given by T\^0&=&[diag]{}([**X\_1**]{}, [**X\_2**]{}, [**X\_2**]{}, [**X\_2**]{}, y\_1, y\_1, y\_2, y\_2, y\_2, y\_2, y\_2, y\_3, y\_3, y\_3, y\_3,y\_3, y\_4, y\_4, y\_4, y\_5, y\_5)  ,    \
T\^&=&[diag]{}([**X\_3**]{}, [**X\_3**]{}, y\_6,y\_6, y\_7,y\_7, y\_2, y\_2, y\_3, y\_3, y\_3, 