strength function.

However, as the mass of nuclei increases, the relative importance of the Landau damping may change. Accordingly, 2p2h states may also contribute to the global profile of the strength function. Therefore, it is very important to investigate how the difference between the damping process of light nuclei and that of heavy nuclei does affect the properties of the fluctuation of the strength function.

In this paper, we study the isoscalar (IS) GQR of $^{208}$Pb, where the strength function is calculated with the second TDA in the same manner as in $^{40}$Ca, and study the fluctuation of the strength function by means of the local scaling dimension. Comparing results with those of $^{40}$Ca we would like to clarify which properties of the damping process are reflected in the fluctuation of the strength function and make clear the physical origin of the difference.

This paper is organized as follows: In Sec. \[sec:lsd\], we briefly explain the local scaling dimension. The strength function for IS GQR in $^{208}$Pb is calculated in Sec. \[sec:numerical\], where the adopted Hamiltonian and the model space are shown. In Sec. \[sec:measures\], we discuss the nearest-neighbor level spacing distribution, $\Delta_3$ statistics as well as a histogram of 