A one-body operator represented by a spherical tensor of rank \( \lambda \) is given as $$ O_{\mu}^{\lambda} = \sum_{pq} \langle p \vert O_{\mu}^{\lambda} \vert q \rangle a^{\dagger}_pa_q, $$ meaning that when we compute a transition amplitude $$ \langle \Psi_{\delta} \vert O_{\mu}^{\lambda} \vert \Psi_{\gamma} \rangle = \sum_{ij} C^{*}_{\delta i} C_{\gamma j} \langle \Phi_i \vert O_{\mu}^{\lambda} \vert \Phi_j\rangle, $$ we need to compute $$ \langle \Phi_i \vert O_{\mu}^{\lambda} \vert \Phi_j\rangle. $$