Evolution of the isoscalar giant monopole resonance in the Ca isotope chain

Two recent studies of the evolution of the isoscalar giant monopole resonance (ISGMR) within the calcium isotope chain report conflicting results. One study suggests that the monopole resonance energy, and thus the incompressibility of the nucleus $K_{A}$ increase with mass, which implies that $K_{\tau}$, the asymmetry term in the nuclear incompressibility, has a positive value. The other study reports a weak decreasing trend of the energy moments, resulting in a generally accepted negative value for $K_{\tau}$. An independent measurement of the central region of the ISGMR in the Ca isotope chain is provided to gain a better understanding of the origin of possible systematic trends. Inelastically scattered $\alpha$ particles from a range of calcium targets ($\mathrm{^{40,42,44,48}Ca}$), observed at small scattering angles including 0$^\circ$, were momentum analyzed in the K600 magnetic spectrometer at iThemba LABS, South Africa. Monopole strengths spanning an excitation-energy range between 9.5 and 25.5 MeV were obtained using the difference-of-spectra (DoS) technique. The structure of the $E0$ strength distributions of $^{40,42,44}$Ca agrees well with the results from the previous measurement that supports a weak decreasing trend of the energy moments, while no two datasets agree in the case of $^{48}$Ca. Despite the variation in the structural character of $E0$ strength distribution from different studies, we find for all datasets that the moment ratios, calculated from the ISGMR strength in the excitation-energy range that defines the main resonance region, display at best only a weak systematic sensitivity to a mass increase. Different trends observed in the nuclear incompressibility are caused by contributions to the $E0$ strength outside of the main resonance region, and in particular for high excitation energies.