interval 9 - 13 MeV. The Landau damping width $\Gamma_{\rm L}$ may be evaluated in terms of a smoothed profile of the strength function plotted with the dotted curve in Fig. \[fig\_tdastr\]. Its FWHM reads 0.21 MeV. On the other hand, if we closely look at Fig. \[fig\_tdastr\], we find that there is the second largest peak just below the largest one and that these two levels dominate the whole structure. The level spacing between these two levels can be considered as a typical spreading of strength and may be a more direct quantitative measure of the Landau damping width $\Gamma_{\rm L}$: The level spacing 0.18 MeV gives $\Gamma_{\rm L}=0.18$ MeV.

### damping due to 2p2h states

The Landau damping width $\Gamma_{\rm L}=0.18$ MeV is not enough to explain the total width $\Gamma=0.63$ MeV of Sec. \[sec:numerical\]. Then, we would like to study a role of 2p2h states in the damping process, namely, the fragmentation of the GQR TD state located at $E=10.7$ MeV in Fig. \[fig\_tdastr\] over 2p2h states. We shall investigate the damping width $\Gamma_2$ caused by the coupling to 2p2h states. To estimate this width, we perform a calculation where we include only the GQR TD state 