For a two-body state where we couple two angular momenta \( j_1 \) and \( j_2 \) to a final angular momentum \( J \) with projection \( M_J \), we can define a similar transformation in terms of the Clebsch-Gordan coeffficients $$ \psi_{(j_1j_2)JM_J}=\sum_{m_{j_1}m_{j_2}}\langle j_1m_{j_1}j_2m_{j_2}|JM_J\rangle\psi_{n_1j_1m_{j_1};l_1s_1}\psi_{n_2j_2m_{j_2};l_2s_2}. $$ We will write these functions in a more compact form hereafter, namely, $$ |(j_1j_2)JM_J\rangle=\psi_{(j_1j_2)JM_J}, $$ and $$ |j_im_{j_i}\rangle=\psi_{n_ij_im_{j_i};l_is_i}, $$ where we have skipped the explicit reference to \( l \), \( s \) and \( n \). The spin of a nucleon is always \( 1/2 \) while the value of \( l \) can be deduced from the parity of the state. It is thus normal to label a state with a given total angular momentum as \( j^{\pi} \), where \( \pi=\pm 1 \).