would like to choose $\omega$ as large as possible since we do not want to wash out the fluctuations at smaller energy scales. Figure \[fig\_fwhm\] shows the FWHM of the smoothed strength function $\tilde{S}(E)/\tilde{\rho}(E)$ as the function of the smoothing width $\omega$. The linear increase of the FWHM at large values of $\omega \agt 0.6$ MeV indicates that the value of $\omega$ is too large, while with smaller values $\omega \alt 0.5$ MeV the FWHM stays at an approximately constant value, reflecting the total width. We therefore adopt 0.5 MeV as the value of the smoothing width $\omega$ in order to satisfy the above requirements.

We use the equidistant energy level ${\bar E}_i$ in Eq. (\[eq\_norstrfun\]), namely, ${\bar E}_i=id$, where $d$ denotes the average level spacing. Finally, we adopted the energy range from 9.9 MeV to 13.1 MeV, where 3321 levels are included.

![ FWHM of the smoothed strength function $\tilde{S}(E)/\tilde{\rho}(E)$ of IS GQR in $^{208}$Pb as a function of smoothing width $\omega$ used in the Strutinsky method. The dotted line is fitted to data and gives $\sim 0.98\omega+0.2$. []{data-label="fig_fwhm"}](fig5.eps){width="6cm"}

![ Normalized strength function Eq. (\[eq\_norstrfun\]) of IS GQR in$^{208}$Pb. Smoothing width $\omega=0.5$ MeV was used. []{data-label="fig_norstrfun"}](fig6.eps){width="6cm"}

The normalized strength 