and 2p2h states, where the coupling between the GQR TD state and 2p2h states as well as the interaction among 2p2h states are taken into account.

![ Strength function by neglecting all TD states except the GQR TD state. 3342 2p2h states lying in 9 MeV - 13 MeV are considered. See Fig. \[fig\_strfun\] for the dotted curve. []{data-label="fig_GQRTDstr"}](fig10.eps){width="6cm"}

Figure \[fig\_GQRTDstr\] shows the resulting strength function. The estimated FWHM is 0.41 MeV, i.e., $\Gamma_2=0.41$ MeV.

If the Landau damping and the 2p2h damping are independent of each other, and neighboring TD states around the GQR TD states also have the same spreading width as $\Gamma_2$, the following approximate relation holds: $$\Gamma\simeq\Gamma_{\rm L}+
\Gamma_2.
\label{Gamma}$$ The values, $\Gamma_{\rm L}=0.18$ MeV and $\Gamma_2=0.41$ MeV, estimated above indeed satisfy this relation. Consequently, the total width $\Gamma=0.63$ MeV is approximately explained as a sum of the Landau damping width $\Gamma_{\rm L} $ and the 2p2h damping width $\Gamma_2$.

The importance of the 2p2h damping is contrasted with the case of $^{40}$Ca, where the total width can be explained essentially by the Landau damping width, i.e., $\Gamma\simeq \Gamma_\text{L}$.

Spreading width of 1p1h states and 2p2h states {#sec:spreading_width}
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For the case of $^{40}$Ca, the strength 