Nuclear incompressibility parameters evaluated from isoscalar giant monopole resonance of $N=Z$, $A=100,132$ nuclide and Sn isotopes

Abstract: The isoscaler giant monopole resonances (ISGMR) are computed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory (Cb-TDHFB) with five kinds of Skyrme parameter sets (SGII, SkM$^*$, SLy4, SkT3 and SkI3). To extract the nuclear matter property from finite system, ISGMRs of $N$=$Z$ ($Z$=20 - 50), isobar even-even nuclide for $A$=100, 132 and Sn isotopes are analysed systematically. The magnitude relation of nuclear incompressibility-parameter ($K_\infty$) among Skyrme parameter sets, can be corresponded to the peak positions of GMR in spherical isotopes over $A$=80. The parameters ($K_{\rm surf}, K_\tau$ and $K_{\rm Coul}$) which appear in expansion of the finite nucleus incompressibility $K_A$, are determined for each Skyrme parameter. From the comparison experimental data whole mass region and the present results, they indicate that the isospin dependent term $K_\tau$ is filtered as -305$\pm$10 MeV. The incompressibility parameters of {\it infinite} system corresponding to our results is $K_\tau^\infty$=-340$\pm$35, $K_\infty$=225$\pm$11, and $K_{\rm sym}$=-138$\pm$18 MeV.