ISGMR $E_{ave}=14.453$ MeV is essentially in agreement with the measured value of $14.17\pm 0.28$ MeV for the ISGMR in $^{208}$Pb [@You99] (a more recent experimental value of $13.96\pm 0.20$ MeV was extracted in Ref. [@You04]). The agreement will become much better if the two-body spin-orbit and the two-body Coulomb interactions are taken into account in the continuum-RPA calculations since the net effect of the two interactions in RPA reduces the centroid energy of ISGMR in $^{208}$Pb by about $300$ keV [@Sil06]. These features imply that the default Skyrme parameter set MSL0 can give a good description for the ISGMR in $^{208}$Pb. Furthermore, one can see from Fig. \[XEaPb208\] that, within the uncertain ranges considered here for the macroscopic quantities, the ISGMR energies display a very strong positive correlation with $K_{0}$ as expected. On the other hand, however, the ISGMR energies also exhibit moderate negative correlations with both $L$ and $m_{s,0}^{\ast }$ while weak dependence on the other macroscopic quantities. These results indicate that the uncertainties of $L$ and $m_{s,0}^{\ast }$ may significantly influence the extraction of $K_{0}$ by comparing the theoretical value of the ISGMR energies of $^{208}$Pb from SHF + RPA calculations with the experimental measurements.

![(Color online) SHF 