will affect our results. Furthermore, in the following calculations, the sum rules $m_{k} $ are obtained by integrating the RPA strength from excitation energy $E_{x}=5$ MeV to $E_{x}=35$ MeV in Eq. (\[RPAmoment\]).

Isospin scalar giant monopole resonance in $^{208}$Pb
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![(Color online) The ISGMR energies of $^{208}$Pb obtained from SHF + continuum-RPA calculations with MSL0 by varying individually $L$ (a), $G_{V}$ (b), $G_{S}$ (c), $E_{0}(\protect\rho _{0})$ (d), $E_{\text{\textrm{sym}}}(\protect\rho _{0})$ (e), $K_{0}$ (f), $m_{s,0}^{\ast }$ (g), $m_{v,0}^{\ast
} $ (h), $\protect\rho _{0}$ (i), and $W_{0}$ (j). The three lines from upper to lower in each panel correspond to $E_{sca}$, $E_{ave}$, and $E_{con} $, respectively.[]{data-label="XEaPb208"}](XEaPb208.eps)

Shown in Fig. \[XEaPb208\] are the ISGMR energies, i.e., $E_{sca}$, $E_{ave}$, and $E_{con}$ of $^{208}$Pb obtained from SHF + continuum-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 $W_{0}$, namely, varying one quantity at a time while keeping all the others at their default values in MSL0. Firstly, one can see clearly the ordering of $E_{sca}\geq
E_{ave}\geq E_{con}$ as expected. In particular, for the default parameters in MSL0, we obtain $E_{sca}=14.962$ MeV, $E_{ave}=14.453$ MeV, and $E_{con}=14.338$ MeV. We note that the centroid energy of 