the present work, we choose the spherical closed-shell doubly-magic nuclei $^{208}$Pb, $^{100}$Sn, and $^{132}$Sn. Thus, we do not include the pairing interaction since it has negligible effects on these spherical closed-shell doubly-magic nuclei considered in this work [@Kha10]. In addition, the two-body spin-orbit and the two-body Coulomb interactions are not taken into account in the present continuum-RPA calculations although the HF calculations include both of the interactions. As pointed out in Ref. [@Sil06], the net effect of the two interactions in RPA decreases the centroid energy of ISGMR in $^{208}$Pb by about $300$ keV. It should be stressed that, in the present work, we do not intend to extract accurately the value of the $K_{0}$ parameter by comparing the measured ISGMR centroid energy with that from HF + continuum-RPA calculations, and our main motivation is to explore the theoretical uncertainty for extracting $K_{0}$. Meanwhile, we are mainly interested in the ISGMR centroid energy difference between $^{100}$Sn and $^{132}$Sn rather than their respective absolute value. Therefore, we do not expect that the two-body spin-orbit and the two-body Coulomb interactions in RPA will significantly change our conclusion and further work is needed to see how exactly the two interactions in continuum-RPA calculations 