using different macroscopic quantities. Furthermore, it should be mentioned that the centroid energy of ISGMR in heavy nuclei are not sensitive to the values of $E_{0}(\rho _{0})$ and $\rho _{0}$ as shown in Fig. \[XEaPb208\], and thus in principle we can adjust $E_{0}(\rho _{0})$ and $\rho
_{0}$ to give better description for the ground state binding energy and charge rms radii of finite nuclei without changing significantly the results of ISGMR and thus the conclusions in the present work.

In order to see the dependence of the detailed structure of ISGMR in $^{208}$Pb on the values of $K_{0}$, $L$ and $m_{s,0}^{\ast }$, we show in Fig. \[SRPAPb208\] the SHF + continuum-RPA response functions of $^{208}$Pb with MSL0 by varying individually $K_{0}$, $L$, and $m_{s,0}^{\ast }$, i.e., $K_{0}=200$ and $270$ MeV, $L=30$ and $90$ MeV, and $m_{s,0}^{\ast }=0.6m$ and $0.9m$. As can be seen in Fig. \[SRPAPb208\], the RPA result displays a single collective peak in each case, consistent with the experimental data [@You04; @Sag07b]. Furthermore, it is seen that varying the value of $K_{0} $ from $200$ MeV to $270$ MeV strongly shifts the single collective peak from about $13.3$ MeV to $15.4$ MeV while varying the value of $L$ 