Recently, the fine structure of the strength distribution of the giant quadrupole resonance (GQR) in $^{208}$Pb [@shevchenko; @shevchenko2; @lacroix] or the Gamow-Teller resonance (GTR) in $^{90}$Zr [@kalmykov] were measured and theoretical analysis has also been done.

In the previous paper [@aiba2], we investigated the GQR in $^{40}$Ca, where the strength function was calculated by means of the second Tamm-Dancoff approximation (TDA), namely, the 1p1h and 2p2h model space is included. The results of the local scaling dimension analysis were as follows: At small energy scale, the behavior of the local scaling dimension is almost the same as that of the GOE, which exhibits the complexity of 2p2h background states. On the other hand, a clear deviation from the GOE was found at the intermediate energy scale and it was found that this energy corresponds to the spreading width of 1p1h states. Hence, we can say that the spreading width of 1p1h states is detected as deviation from the GOE limit in $^{40}$Ca.

For $^{40}$Ca the Landau damping is important for the damping process of the giant resonance. Namely, the strength is first fragmented over a wide range of 1p1h states, and this fragmentation characterizes a global profile of the total 