We have also defined matrix elements in the coupled basis, the so-called \( J \)-coupled scheme. In this case the two-body wave function for two neutrons outside \( {}^{16}\mbox{O} \) is written as $$ |^{18}\mathrm{O}\rangle_J =|(ab)JM\rangle = \left\{a^{\dagger}_aa^{\dagger}_b\right\}^J_M|^{16}\mathrm{O}\rangle=N_{ab}\sum_{m_am_b}\langle j_am_aj_bm_b|JM\rangle|\Phi^{ab}\rangle, $$ with $$ |\Phi^{ab}\rangle=a^{\dagger}_aa^{\dagger}_b|^{16}\mathrm{O}\rangle. $$ We have now an explicit coupling order, where the angular momentum \( j_a \) is coupled to the angular momentum \( j_b \) to yield a final two-body angular momentum \( J \). The normalization factor is $$ N_{ab}=\frac{\sqrt{1+\delta_{ab}\times (-1)^J}}{1+\delta_{ab}}. $$