Nikolaev and Michel have obtained the same result.[@Nikolaev03]

  ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                        RXS amplitude                                
  ------------ -------------------------------------------------------------------------- -------------------------------------------------------------------------- --------------------------------------------------------------------------
                                              Longitudinal                                                               Transverse 1                                                               Transverse 2

  dipole             -${\rm i}\alpha_1(\omega) \langle \psi_0|J_{z}|\psi_0 \rangle              -${\rm i}\alpha_1(\omega) \langle \psi_0|J_{x}|\psi_0 \rangle              -${\rm i}\alpha_1(\omega) \langle \psi_0|J_{y}|\psi_0 \rangle
                  (\mbox{\boldmath{$\epsilon$}}' \times \mbox{\boldmath{$\epsilon$}})_z$     (\mbox{\boldmath{$\epsilon$}}' \times \mbox{\boldmath{$\epsilon$}})_x$     (\mbox{\boldmath{$\epsilon$}}' \times \mbox{\boldmath{$\epsilon$}})_y$

                        $+ \alpha_2(\omega) \langle \psi_0|Q_{5}|\psi_0 \rangle                    $+ \alpha_2(\omega) \langle \psi_0|Q_{3}|\psi_0 \rangle                    $+ \alpha_2(\omega) \langle \psi_0|Q_{4}|\psi_0 \rangle
                    P_5 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$          P_3 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$          P_4 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$

  quadrupole             $\alpha_2(\omega) \langle \psi_0|Q_{5}|\psi_0 \rangle                      $\alpha_2(\omega) \langle \psi_0|Q_{3}|\psi_0 \rangle                      $\alpha_2(\omega) \langle \psi_0|Q_{4}|\psi_0 \rangle
                    P_5 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$          P_3 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$          P_4 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$

  octupole               $\alpha_2(\omega) \langle \psi_0|Q_{5}|\psi_0 \rangle                      $\alpha_2(\omega) \langle \psi_0|Q_{3}|\psi_0 \rangle                      $\alpha_2(\omega) \langle \psi_0|Q_{4}|\psi_0 \rangle
                    P_5 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$          P_3 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$          P_4 (\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}})$
  ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

![\[fig.azim\] Azimuthal-angle dependence of the RXS spectra from the triple-**k** AFO phases with ${\textbf G}=(003)$. (a) Longitudinal ordering. The open circles and filled triangles are experimental data, and the solid and broken lines are the calculated results, in the $\sigma$-$\sigma'$ and $\sigma$-$\pi'$ channels, respectively.[@Caciuffo03] (b) Transverse orderings in the $\sigma$-$\pi'$ channel. No RXS signal is expected from these orders in the $\sigma$-$\sigma'$ channel. The solid and broken lines are the calculated results for the two transverse orders. ](Fig.4.eps){width="7.50cm"}

Now we discuss the energy profiles. In order to calculate them, we need the wavefunctions in the 