\[XKsat2\], leading additional decrement of $E_{ave}$ with $m_{s,0}^{\ast }$ for the neutron-rich nucleus $^{132}$Sn.

![(Color online) Same as Fig. \[XEaPb208\] but for the ISGMR centroid energy $E_{ave}$ of $^{100}$Sn and $^{132}$Sn. The results of $^{100}$Sn shift down by $1.5$ MeV for a more clear comparison with those of $^{132}$Sn.[]{data-label="XEcSn100132"}](XEcSn100132.eps)

![Same as Fig. \[XEaPb208\] but for the ISGMR centroid energy difference between $^{100}$Sn and $^{132}$Sn.[]{data-label="dEcSn100132"}](dEcSn100132.eps)

It is instructive to see the ISGMR centroid energy difference between $^{100} $Sn and $^{132}$Sn, which is shown in Fig. \[dEcSn100132\] 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 $W_{0}$. It is very interesting to see from Fig. [dEcSn100132]{} that, within the uncertain ranges considered here for the macroscopic quantities, the ISGMR centroid energy difference displays a very strong correlation with $L$. However, on the other hand, the ISGMR centroid energy difference exhibits only moderate correlations with $m_{s,0}^{\ast }$ and $m_{v,0}^{\ast }$ while weak dependence on the other macroscopic quantities. These features imply that the ISGMR centroid energy difference between $^{100}$Sn and $^{132}$Sn provides a potential probe of the $L$ parameter. Furthermore, it is seen that the ISGMR centroid energy difference displays opposite correlation 