and (\[eq.Tp\]) that the dipole ordering induces the quadrupole moment but no octupole moment. Note that, if the quadrupole ordering is primary, no dipole moment is induced, because the doubly-degenerate eigenstates of $Q_p$ are the eigenstates of $\pm j_1$ of $J_p$.

RXS spectra
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Irrespective of whether the octupole or quadrupole ordering is realized, RXS amplitudes are generated at each site, according to Eq. (\[eq.Mtilde.2\]). They are proportional to $q_1 \alpha_2(\omega)(P_3+P_4+P_5)$ for the simultaneous eigenstate of $T_{111}$ and $Q_{111}$, to $q_1 \alpha_2(\omega)(P_3-P_4-P_5)$ for the simultaneous eigenstate of $T_{\overline{1}11}$ and $Q_{\overline{1}11}$, to $q_1 \alpha_2(\omega)(-P_3+P_4-P_5)$ for the simultaneous eigenstate of $T_{1\overline{1}1}$ and $Q_{1\overline{1}1}$, and to $q_1 \alpha_2(\omega)(-P_3-P_4+P_5)$ for the simultaneous eigenstate of $T_{11\overline{1}}$ and $Q_{11\overline{1}}$. On the scattering vector ${\textbf G}=(h h \ell)$ with $h + \ell=odd$, these amplitudes are summed up with a positive sign for sublattices 1 and 2 and with a negative sign for sublattices 3 and 4. Therefore, the total RXS amplitude becomes proportional to $q_1\alpha_2(\omega)P_5$ for the longitudinal order, while they are proportional to $q_1\alpha_2(\omega)P_3$ and $q_1\alpha_2(\omega)P_4$ for the two transverse orders. Note that a similar analysis is applied to the dipole ordering. In this case, both the dipole and quadrupole terms contribute to the amplitude. These 