and $M_5$ edges are displayed with several choices of $\Gamma$ values in Fig. \[fig.alpha\_2\]. The origin of the energy is adjusted such that the peak of the RXS spectrum is located at the experimental peak position. Since there is no reliable estimation for the $\Gamma$ value, we choose three typical values $\Gamma=0.01, 0.5$ and $2.0$ eV. The spike-like curves with $\Gamma=0.01$ eV directly reflect the multiplet splittings of the intermediate states. For the $M_4$ edge, the choice $\Gamma=0.5$ eV makes a multi-peak-structure line-shape. It merges into a single-peak structure around $\Gamma \simeq 1.0$ eV. The choice $\Gamma=2.0$ eV corresponds to one of better fittings with the experimental line shape.[@Paixao02; @Caciuffo03] The core-level energy is adjusted such that the calculated peak at the $M_4$ edge with $\Gamma=2$ eV coincides with the experimental one. Paixao [*et al*]{}. reported that the line shape is well fitted by a Lorentzian-squared rather than a Lorentzian one.[@Paixao02] As shown above, the line shape is basically determined by the multiplet structure, which is smeared by the life-time broadening. Whether it looks Lorentzian-squared or Lorentzian seems unimportant. As for the spectra at the $M_{5}$ edge, their shape depends rather sensitively on the value of $\Gamma$ compared to that 