Compression-mode resonances in the calcium isotopes and implications for the asymmetry term in nuclear incompressibility

Recent data on isoscalar giant monopole resonance (ISGMR) in the calcium isotopes ${}^{40,44,48}$Ca have suggested that $K_{\tau }$, the asymmetry term in the nuclear incompressibility, has a positive value. A value of $K_{\tau }>0$ is entirely incompatible with present theoretical frameworks and, if correct, would have far-reaching implications on our understanding of myriad nuclear and astrophysical phenomena. This paper presents results of an independent ISGMR measurement with the ${}^{40,42,44,48}$Ca($\alpha ,{\alpha }^{\mathrm{\prime }}$) reaction at $E_{\alpha }=386$ MeV. These results conclusively discount the possibility of a positive value for $K_{\tau }$, and are consistent with the previously-obtained values for this quantity.