Differential analysis of incompressibility in neutron-rich nuclei

Both the incompressibility K-A of a finite nucleus of mass A and that (K-infinity) of infinite nuclear matter are fundamentally important for many critical issues in nuclear physics and astrophysics. While some consensus has been reached about K-infinity, accurate theoretical predictions and experimental extractions of K-tau characterizing the isospin dependence of K-A have been very difficult. We propose a differential approach to extract K-tau and K-infinity independently from the K-A data of any two nuclei in a given isotope chain. Applying this method to the K-A data from isoscalar giant monopole resonances (ISGMR) in even-even Pb, Sn, Cd, and Ca isotopes taken by Garg et al. at the Research Center for Nuclear Physics (RCNP), Osaka University, Japan, we find that the Cd-106 - Cd-116 and Sn-112 - Sn-124 pairs having the largest differences in isospin asymmetries in their respective isotope chains measured so far provide consistently the most accurate up-to-date K-tau value of K-tau = -616 +/- 59 MeV and K-tau = -623 +/- 86 MeV, respectively, largely independent of the remaining uncertainties of the surface and Coulomb terms in expanding K-A, while the K-infinity values extracted from different isotopes chains are all well within the current uncertainty range of the community consensus for K-infinity. Moreover, the size and origin of the "soft Sn puzzle" is studied with respect to the "stiff Pb phenomenon." It is found that the latter is favored due to a much larger (by approximate to 380 MeV) K-tau for Pb isotopes than for Sn isotopes, while K-infinity from analyzing the K-A data of Sn isotopes is only about 5 MeV less than that from analyzing the Pb data.