Why is the equation of state for tin so soft?

The distribution of isoscalar monopole strength in the neutron-even ${}^{112-124}\mathrm{Sn}$ isotopes has been computed using a relativistic random-phase-approximation approach. The accurately-calibrated model used here (“FSUGold”) has been successful in reproducing both ground-state observables as well as collective excitations—including the giant monopole resonance (GMR) in ${}^{90}\mathrm{Zr}$, ${}^{144}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$. Yet this same model significantly overestimates the GMR energies in the Sn isotopes. It is argued that the question of “Why is tin so soft?” becomes an important challenge to the field and one that should be answered without sacrificing the success already achieved by several theoretical models.

Figure 1

Distribution of isoscalar monopole strength predicted by the FSUGold model of Ref. [10]. The inset includes a comparison against the experimental centroid energies reported in Ref. [14], with the solid line providing the best fit to the theoretical predictions.

Figure 2

Comparison between the distribution of isoscalar monopole strength in all neutron-even ${}^{112}\mathrm{Sn}$-${}^{124}\mathrm{Sn}$ isotopes extracted from experiment (black solid squares) and the theoretical predictions of the FSUGold (blue solid line) and NL3 (green dashed line) models.

Figure 3

Comparison between the GMR centroid energies ($m_1/m_0$) in all neutron-even ${}^{112}\mathrm{Sn}$-${}^{124}\mathrm{Sn}$ isotopes extracted from experiment (black solid squares) and the theoretical predictions of the FSUGold (blue up-triangles) and NL3 (green down-triangles) models. Also shown (filled red circles) are results from the Texas A&M group [14, 35, 36] for the cases of ${}^{112}\mathrm{Sn}$, ${}^{116}\mathrm{Sn}$, and ${}^{124}\mathrm{Sn}$.