Investigating a possible positive value of $K_\tau$, and implications for the symmetry energy

The isoscalar giant monopole resonances (ISGMR) in isotopic chains with large neutron-excess provide excellent constraints for $K_\tau$, the asymmetry term in the nuclear incompressibility. $K_\tau$ has been extracted from the ISGMR in tin and cadmium to be $-550 \pm 100$ MeV, and is critical input to the symmetry energy of nuclear matter. Recent reports on the ISGMR in $^{40,44,48}$Ca contradict the prior studies, concluding that $K_\tau > +500$ MeV. A simultaneous study of the ISGMR in $^{40,42,44,48}$Ca was thus completed at the Research Center for Nuclear Physics. The spectrograph, Grand Raiden, allowed for measurements of background-free angular distributions for inelastic scattering of $386$ MeV $\alpha$-particles. Multipole decomposition analyses isolated the ISGMR strength, and the energies of the compressional mode were extracted. The results and implications will be discussed.