a Only statistical uncertainties are included; systematic errors, mostly from DWBA calculations, are ∼ 15%. than the nuclear incompressibility, requiring a modification of the scaling relationship given in Eq. 7? There have been several attempts to explain this anomaly. One of the earliest was by Civitarese et al. [71] to estimate the effect of pairing correlations on the energy of the ISGMR. The shifts obtained for the ISGMR energies of 100–150 keV across the Sn isotopic chain were insufficient to explain the experimental data. Piekarewicz and Centelles [72] have constructed a hybrid model having the same incompressibility coefficient ( K$_{∞}$ =230 MeV) as the FSUGold [73] while preserving the stiff symmetry energy of NL3 [74]. This results in a considerably softer incompressibility coefficient for neutron-rich matter and produces a significant improvement in agreement with the experimental data on the ISGMR’s in the Sn isotopes. However, as the authors point out, while the improvement in case of the Sn isotopes is unquestionable, an important problem remains: the hybrid model underestimates the ISGMR centroid energy in $^{208}$Pb by almost 1 MeV, suggesting that the rapid softening 18 TABLE IV: Various moment ratios for the ISGMR strength distributions in the Sn isotopes. All moments have been calculated over E$_{x}$ = 10.5–20.5 MeV. The quoted EWSR values are from the strength observed within this energy range. The results from TAMU work, where available, are provided for comparison [19, 21]. Target m 1 m 0 (MeV) √ m 3 m 1 (MeV) √ m 1 m$_{−}$ 1 (MeV) EWSR a Reference $^{112}$Sn 16 . 2 ± 0 . 1 16 . 7 ± 0 . 2 16 . 1 ± 0 . 1 0 . 73 ± 0 . 04 This work 15 . 43 +0 . 11 − 0 10 16 . 05 +0 . 26 − 0 14 15 . 23 +0 . 10 − 0 10 1 . 16 +0 . 13 − 0 18 TAMU $^{114}$Sn 16 . 1 ± 0 . 1 16 . 5 ± 0 . 2 15 . 9 ± 0 . 1 0 . 86 ± 0 . 05 This work $^{116}$Sn 15 . 8 ± 0 . 1 16 . 3 ± 0 . 2 15 . 7 ± 0 . 1 0 . 86 ± 0 . 05 This work 15 . 85 ± 0 . 20 1 . 12 ± 0 . 15 TAMU $^{118}$Sn 15 . 8 ± 0 . 1 16 . 3 ± 0 . 1 15 . 6 ± 0 . 1 0 . 73 ± 0 . 04 This work $^{120}$Sn 15 . 7 ± 0 . 1 16 . 2 ± 0 . 2 15 . 5 ± 0 . 1 0 . 78 ± 0 . 05 This work $^{122}$Sn 15 . 4 ± 0 . 1 15 . 9 ± 0 . 2 15 . 2 ± 0 . 1 0 . 85 ± 0 . 05 This work $^{124}$Sn 15 . 3 ± 0 . 1 15 . 8 ± 0 . 1 15 . 1 ± 0 . 1 0 . 77 ± 0 . 05 This work 14 . 50 +0 . 14 − 0 14 14 . 96 +0 . 10 − 0 11 14 . 33 +0 . 17 − 0 14 1 . 04 +0 . 11 − 0 11 TAMU