those of $^{208}$Pb for the sake of comparison.

Figure \[fig\_nns\] shows the NND. For both nuclei the NND follows the Wigner distribution well. We present the strength distribution in Fig. \[fig\_strdis\] where a histogram of the square-root of normalized strengths is plotted. We also find that for both $^{208}$Pb and $^{40}$Ca the distribution follows the Porter-Thomas one rather well. These two figures indicate that for both nuclei the fluctuation of the strength as well as that of the energy level spacing is governed by the GOE at least at small energy scale limit as expected.

Figure \[fig\_delta3\] shows the $\Delta_3$ statistics. We again find that at small energy range the $\Delta_3$ follows the GOE line for both $^{208}$Pb and $^{40}$Ca, although at intermediate energy scales, $L_{\rm max}\simeq 20$ or 15 for $^{208}$Pb or $^{40}$Ca, respectively, the $\Delta_3$ starts to deviate from the GOE line to upward.

![ The histogram of the square-root of normalized strengths $\bar{S}_i^{1/2}$ associated with IS GQR in (a) $^{40}$Ca and (b) $^{208}$Pb. The solid curve represents the Porter-Thomas distribution which becomes a Gaussian when plotted as a function of $\bar{S}_i^{1/2}$. See the caption of Fig. \[fig\_nns\] for the number of considered levels and also see Sec. 