Giant resonances in Ca ,48 40 , 68 Ni, 90 Zr, 116 Sn, 144 Sm, and 208 Pb

We present results of centroid energies ${E}_{\mathrm{CEN}}$, of the isoscalar ($T=0$) and isovector ($T=1$) giant resonances of multipolarities $L=0--3$ in $^{40,48}\mathrm{Ca}, ^{68}\mathrm{Ni}, ^{90}\mathrm{Zr}, ^{116}\mathrm{Sn}, ^{144}\mathrm{Sm}$, and $^{208}\mathrm{Pb}$, calculated within the fully self-consistent Hartree-Fock-based random phase approximation theory, using 33 different Skyrme-type effective nucleon-nucleon interactions of the standard form commonly adopted in the literature. We compare the results of our theoretical calculations with the available experimental data. We also study the sensitivity of the calculated ${E}_{\mathrm{CEN}}$ to physical properties of nuclear matter (NM), such as effective mass m*/m, nuclear matter incompressibility coefficient ${K}_{\mathrm{NM}}$, enhancement coefficient \ensuremath{\kappa} of the energy weighted sum rule for the isovector giant dipole resonance and symmetry energy at saturation density, associated with the Skyrme interactions used in the calculations. This is done by determining the Pearson linear correlation coefficient between the calculated ${E}_{\mathrm{CEN}}$ and a certain NM property. Constraining the values of the NM properties, by comparing the calculated values of ${E}_{\mathrm{CEN}}$ to the experimental data, we find that interactions associated with the values of ${K}_{\mathrm{NM}}=210--240\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ and $\ensuremath{\kappa}=0.25--0.70$ best reproduce the experimental data.