results are summarized in Table \[table.6\]. For the transverse case, our present treatment could be extended applying to the RXS spectra detected at Np $M_4$ edges in U$_{0.75}$Np$_{2}$O$_2$.[@Wilkins04] In this compound, the spectra may be interpreted as a consequence brought about by the transverse type of triple-**k** AFO ordering driven by the same ordering pattern at U sites.

Polarization dependences become particularly simple for ${\textbf G}=(00 \ell)$ ($\ell=$ odd) in the octupole and quadrupole orderings. They are explicitly written in the scattering geometry shown in Fig. \[fig.geom\] as $P_3=0$, $P_4=0$, $P_5=(\sqrt{3}/2)\sin 2\psi$ in the $\sigma-\sigma'$ channel, while $P_3=(\sqrt{3}/2)\cos\theta\cos\psi$, $P_4=(\sqrt{3}/2)\cos\theta\sin\psi$, $P_5=(\sqrt{3}/2)\sin\theta\cos 2\psi$ in the $\sigma-\pi'$ channel. Figure \[fig.azim\] shows the azimuthal-angle dependence of the spectra ${\textbf G}=(003)$ in comparison with the experiment. [@Paixao02; @Caciuffo03] The experimental data are well fitted by $\sin^2 2 \psi$ in the $\sigma$-$\sigma'$ channel, and $\sin^2 \theta \cos^2 2 \psi$ in the $\sigma$-$\pi'$ channel. The two transverse orders cannot reproduce the experimental curves, as seen from panel (b). Paixão *et al*. and Caciuffo *et al*. analyzed their experimental data and concluded that the longitudinal order gives rise to this dependence.[@Paixao02; @Caciuffo03] The present analysis confirms their result. Note that, based on a group theoretical point of view, 