largest peak, the FWHM is more appropriate than the standard deviation  [@bertsch2]. Thus, we use the FWHM as a measure of the total width $\Gamma$ of the strength function, which gives $\Gamma=0.63$ MeV.

Hereafter, when we estimate the value of the FWHM, the same procedure as above is adopted, namely, we calculate the FWHM for the smooth strength function by means of the Strutinsky method with the smoothing width 0.2 MeV.

Fluctuation at small scale {#sec:measures}
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![ The nearest-neighbor level spacing distribution for (a) $^{40}$Ca and (b) $^{208}$Pb. For $^{208}$Pb 3321 levels between 9.9 MeV and 13.1 MeV, while for $^{40}$Ca 804 levels between 20 MeV and 30 MeV are considered. Level spacings were unfolded by the Strutinsky method with a smoothing width 0.5 MeV for $^{208}$Pb and 5.0 MeV for $^{40}$Ca, respectively. The solid curve represents the Wigner distribution. []{data-label="fig_nns"}](fig2.eps){width="9.2cm"}

Before going to the detailed discussion of the local scaling dimension, we briefly show the results for other fluctuation measures: the nearest-neighbor level spacing distribution (NND), the strength distribution, and $\Delta_3$ statistics. Here, the NND and the strength distribution are measures characterizing the fluctuation at small energy scale limit. We present the results of $^{40}$Ca as well as 