to $|A^0_{2}\rangle$ and $|A^0_{i}\rangle$ $(i=4,6,8,11-15)$, respectively. The first eight states block-diagonalize the transition matrix to four $2 \times 2$ submatrices, and the other seventeen states give eigenstates.\
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There are eighteen singly-charged states with the electric charge $+1$ among all the two-body states. The charge conservation ensures that these states are composed of a subset among all the states with various electric charges. The corresponding high-energy transition matrix is consequently (block-) diagonalized by the following states: |A\_1\^+&=&(\^+\_r\^0+\^+\_i\^0)/ ,\
|A\_2\^+&=&(\^[++]{}\^-+ \^+\_r\^0+\^+\_i\^0)/2  ,\
|A\_3\^+&=&(\^+\_r\^0-\^+\_i\^0)/ ,\
|A\_4\^+&=&(\^[++]{}\^-+ \^+\_r\^0-\^+\_i\^0)/2  ,\
|A\_5\^+&=&(\^[++]{}\^- -\^+\_r\^0-\^+\_i\^0+2\^+ \_r\^0)/2 ,\
|A\_6\^+&=&(\^[++]{}\^- - \^+\_r\^0+\^+\_i\^0+2\^+ \_r\^0)/2 ,\
|A\_7\^+&=&(\^[++]{}\^–\^+\_r\^0-\^+\_i\^0-2\^+\_r\^0)/2 ,\
|A\_8\^+&=&(\^[++]{}\^- -\^+\_r\^0+\^+\_i\^0-2\^+\_r\^0) /2 ,\
|A\_[9]{}\^+&=&(\^+\_r\^0+\^+\_i\^0)/ ,\
|A\_[10]{}\^+&=&(\^+\_r\^0-\^+\_i\^0)/ ,\
|A\_[11]{}\^+&=& (\^[++]{}\^–2\^+\_r\^0-\^+\_r\^0-\^+\_i\^0-\^+\_r\^0+\^+\_i\^0)/3 ,\
|A\_[12]{}\^+&=& (\^+\_r\^0+\^+\_i\^0+\^+\_r\^0+\^+\_i\^0)/ ,\
|A\_[13]{}\^+&=& (\^+\_r\^0-\^+\_i\^0+ \^+\_r\^0 -\^+\_i\^0)/ ,\
|A\_[14]{}\^+&=& (4\^[++]{}\^-+4\^+\_r\^0-\^+\_r\^0 -\^+\_i\^0-\^+\_r\^0+\^+\_i\^0)/6  ,\
|A\_[15]{}\^+&=& (\^+\_r\^0+\^+\_i\^0-\^+\_r\^0+\^+\_i\^0)/2 ,\
|A\_[16]{}\^+&=& (\^+\_r\^0+\^+\_i\^0- \^+\_r\^0-\^+\_i\^0)/ ,\
|A\_[17]{}\^+&=& (\^+\_r\^0-\^+\_i\^0- \^+\_r\^0 +\^+\_i\^0)/ ,\
|A\_[18]{}\^+&=& (2\^[++]{}\^–\^+\_r\^0+\^+\_r\^0 +\^+\_i\^0+\^+\_r\^0-\^+\_i\^0)/3 . The eighteen singly-charged states with the electric charge $-1$ can be obtained by the $C$ transformation for the above states with the charge $+1$.\
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There are eleven doubly-charged two-body states with the electric charge $+2$. We can decompose the subset of the transition matrix for these states to at most $2 \times 2$ matrices by the following linear combination; |A\_1\^[++]{}&=&\^+\^+,\
|A\_2\^[++]{}&=&(\^+\^+ -\^[++]{}\_r\^0)/ ,\
