Isoscalar and Isovector Giant Resonances in Closed Shells Nuclei and Bulk Properties of Nuclear Matter
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NUCLEI Theory
Isoscalar and Isovector Giant Resonances in Closed Shells Nuclei and Bulk Properties of Nuclear Matter S. Shlomo* Cyclotron Institute, Texas A&M University, College Station, Texas, USA Received December 25, 2019; revised December 25, 2019; accepted December 25, 2019
Abstract—Centroid energies, ECEN , of the isoscalar (T = 0) and isovector (T = 1) giant resonances of multipolarities Lm = 0–3 in 40,48 Ca, 68 Ni, 90 Zr, 116 Sn, 144 Sm, and 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 ECEN and each bulk property of nuclear matter (NM), associated with the Skyrme interactions used in the calculations, and determine the sensitivity of ECEN to bulk properties of NM. By comparing the calculated values of ECEN 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∗ /m = 0.70–0.90, incompressibility coefficient, KNM = 210–240 MeV, and the enhancement coefficient of the energy-weighted sum rule of the isovector giant dipole resonance, κ = 0.25–0.70, best reproduce the experimental data. DOI: 10.1134/S1063778820040183
and 208 Pb, by carrying out self-consistent spherical Hartree–Fock (HF)-based random-phaseExperimental and theoretical investigation of struc- approximation (RPA) calculations. We determined ture and excitation of giant resonances in nuclei has the sensitivity of the calculated centroid energies been the subject of interest during the last eight ECEN to bulk nuclear matter properties, by caldecades. In particular, properties of giant resonances culating the Pearson linear correlation coefficient can be used to pin down bulk properties of nuclear between them. For the ECEN of the ISGMR we mater (NM) needed to determine the energy density find strong correlation with the NM incompressibility functional (EDF). We note that the EDF can be used coefficient, KNM , as well as good agreement with to determine the equation of state (EOS) of NM and experimental data. Similarly, between the ECEN of describe properties of nuclei, structure and evolution the isoscalar giant quadrupole resonance and the of stars, and heavy-ion collisions [1–4]. The first nucleon effective mass, m∗ /m, between the ECEN observation of giant resonances [5] has shown a large of the IVGDR and the energy-weighted sum rule peak in the cross section by bombarding U and Th (EWSR) enhancement coefficient for the IVGDR, κ, nuclei with γ rays from a betatron. This was later we obtain strong correlations and good agreement recognized as the isovector giant dipole resonance with experimental data. This allows us to determine (IVGDR). A few decades later, the isoscalar giant constraints on the values of KNM , m∗ /m and κ that quadrupo
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