MeV, namely, about $\pm 16$ MeV for $K_{0}=230$ MeV.

Furthermore, including other uncertainties due to $G_{V}$, $G_{S}$, $E_{0}(\rho _{0})$, $E_{\text{\textrm{sym}}}(\rho _{0})$, $m_{v,0}^{\ast }$, $\rho _{0}$ and $W_{0}$ with empirical values of $G_{V}=0\pm 40$ MeV, $G_{S}=130\pm 10$ MeV, $E_{0}(\rho _{0})=-16\pm 1$ MeV, $E_{\text{\textrm{sym}}}(\rho _{0})=30\pm 5$ MeV, $m_{v,0}^{\ast }=(0.7\pm 0.1)m$, $\rho
_{0}=0.16\pm 0.01$ fm$^{-3}$ and $W_{0}=130\pm 20$ MeV, and assuming all the uncertainties are independent, we can obtain from Fig. \[XEaPb208\] a total uncertainty of about $\pm 0.647$ MeV for the ISGMR centroid energy in $^{208}$Pb, which gives an uncertainty of about $\pm 9\%$ for $K_{0}$, namely, about $\pm 21$ MeV for $K_{0}=230$ MeV.

Isospin scalar giant monopole resonances in $^{100}$Sn and $^{132}$Sn
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To see the isotopic dependence of the ISGMR centroid energy, we study here the spherical closed-shell doubly-magic nuclei $^{100}$Sn and $^{132}$Sn. Shown in Fig. \[XEcSn100132\] are the ISGMR centroid energy $E_{ave}$ of $^{100}$Sn and $^{132}$Sn obtained from SHF + RPA calculations with MSL0 by varying individually $L$, $G_{V}$, $G_{S}$, $E_{0}(\rho _{0})$, $E_{\text{\textrm{sym}}}(\rho _{0})$, $K_{0}$, $m_{s,0}^{\ast }$, $m_{v,0}^{\ast }$, $\rho _{0}$, and $W_{0}$. One can see that the results for neutron-rich nucleus $^{132}$Sn are quite similar to those for $^{208}$Pb as shown in Fig. \[XEaPb208\]. On the other hand, 