Differential analysis of incompressibility in neutron-rich nuclei

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