Isoscalar and Isovector Giant Resonances in Closed Shells Nuclei and Bulk Properties of Nuclear Matter

Abstract

Centroid energies, $E_{\textrm{CEN}}$, of the isoscalar ($T=0$) and isovector ($T=1$) giant resonances of multipolarities $L_{m}=0$–3 in ${}^{\mathrm{40,48}}$Ca, ${}^{\mathrm{68}}$Ni, ${}^{\mathrm{90}}$Zr, ${}^{\mathrm{116}}$Sn, ${}^{\mathrm{144}}$Sm, and ${}^{\mathrm{208}}$Pb, were calculated within the fully self-consistent spherical Hartree–Fock (HF)-based random-phase approximation (RPA) theory, using 33 different energy density functionals associated with Skyrme-type effective nucleon–nucleon interactions of the standard form commonly employed in the literature. We also calculate the Pearson linear correlation coefficients between each $E_{\mathrm{CEN}}$ and each bulk property of nuclear matter (NM), associated with the Skyrme interactions used in the calculations, and determine the sensitivity of $E_{\mathrm{CEN}}$ to bulk properties of NM. By comparing the calculated values of $E_{\textrm{CEN}}$ to the experimental data, we constrain the values of the bulk NM properties. We find that interactions associated with the values of the NM effective mass, $m^{\ast}/m=0.70$–0.90, incompressibility coefficient, $K_{\textrm{NM}}=210$–240 MeV, and the enhancement coefficient of the energy-weighted sum rule of the isovector giant dipole resonance, $\kappa=0.25$–0.70, best reproduce the experimental data.