mechanism of producing the total width of the strength function. Here, using these quantities we would like to discuss the physical origin of the difference between the fluctuation of the strength fluctuation of $^{40}$Ca and that of $^{208}$Pb. Table \[table2\] summarizes the values of the above physical quantities related to the initial stage of the damping process for both $^{40}$Ca and $^{208}$Pb.

We have shown in our previous study [@aiba] that the damping process through the doorway states causes large fluctuations which have characteristic energy scales, and that the fluctuations emerge in the local scaling dimension. For instance, the energy scale of the spreading width $\gamma_{12}$ of the doorway states is the quantity which shows up prior to the other quantities. It is noted, however, the size of the fluctuations depends on the mutual relations among the quantities mentioned above, and indeed we have examined in [@aiba] the relations which are needed to detect the effect of the spreading width $\gamma_{12}$.

                $\Gamma$   $\Gamma_{\rm L}$   $\Gamma_2$   $\gamma_{12}$   $D_{\rm 1p1h}$   $\gamma_{22}$    $d_{\rm 2p2h}$
  ------------ ---------- ------------------ ------------ --------------- ---------------- --------------- ----------------
  $^{40}$Ca       4000           4000            1500          1500             500             5200                     11
  $^{208}$Pb      630            180             410            380             230              750                    1.2

  :  Values of physical quantities 