Differential analysis of incompressibility in neutron-rich nuclei

Abstract

Both the incompressibility \Ka of a finite nucleus of mass A and that ($K_{\infty }$) of infinite nuclear matter are fundamentally important for many critical issues in nuclear physics and astrophysics. While some consensus has been reached about the $K_{\infty }$, accurate theoretical predictions and experimental extractions of $K_{\tau }$ characterizing the isospin dependence of \Ka have been very difficult. We propose a differential approach to extract the \Kt and \Ki independently from the \Ka data of any two nuclei in a given isotope chain. Applying this new method to the \Ka data from isoscalar giant monopole resonances (ISGMR) in even-even Pb, Sn, Cd and Ca isotopes taken by U. Garg {\it et al.} at the Research Center for Nuclear Physics (RCNP), Osaka University, Japan, we find that the ${}^{106}$Cd-${}^{116}$Cd and ${}^{112}$Sn-${}^{124}$Sn pairs having the largest differences in isospin asymmetries in their respective isotope chains measured so far provide consistently the most accurate up-to-date \Kt value of $K_{\tau }=-616\pm 59$ MeV and $K_{\tau }=-623\pm 86$ MeV, respectively, largely independent of the remaining uncertainties of the surface and Coulomb terms in expanding the $K_{\mathrm{A}}$, while the $K_{\infty }$ values extracted from different isotopes chains are all well within the current uncertainty range of the community consensus for $K_{\infty }$. 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 $\sim 380$ MeV) \Kt for Pb isotopes than for Sn isotopes, while the \Ki from analyzing the \Ka data of Sn isotopes is only about 5 MeV less than that from analyzing the Pb data.

More discussions added. Phys. Rev. C in press

References in corpus (9)

• Isotopic dependence of the giant monopole resonance in the even-A ^{112-124}Sn isotopes and the asymmetry term in nuclear incompressibility
• Incompressibility in finite nuclei and nuclear matter
• Incompressibility of neutron-rich matter
• Isoscalar giant resonances in the Sn nuclei and implications for the asymmetry term in the nuclear-matter incompressibility
• Giant Monopole Resonance in even-A Cd isotopes, the asymmetry term in nuclear incompressibility, and the "softness" of Sn and Cd nuclei
• The role of superfluidity in nuclear incompressibilities
• Breathing-mode measurements in Sn isotopes and isospin dependence of nuclear incompressibility
• The Giant Monopole Resonance in Pb isotopes
• Bayesian uncertainty quantification for nuclear matter incompressibility

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