Microscopic study of the isoscalar giant monopole resonance in Cd, Sn, and Pb isotopes

The isoscalar giant monopole resonance (ISGMR) in Cd, Sn, and Pb isotopes has been studied within the self-consistent Skyrme Hartree-Fock + BCS and quasiparticle random phase approximation (QRPA). Three Skyrme parameter sets are used in the calculations (i.e., SLy5, SkM*, and SkP) since they are characterized by different values of the compression modulus in symmetric nuclear matter; namely, K-infinity = 230, 217, and 202 MeV, respectively. We also investigate the effect of different types of pairing forces on the ISGMR in Cd, Sn, and Pb isotopes. The various calculated energies and the strength distributions of the ISGMR are compared with available experimental data. We find that SkP underestimates the various energies for all isotopes due to its low value of the nuclear matter incompressibility; namely, K-infinity = 202 MeV. However, it can give a better description on the constrained energies for Cd isotopes and a reasonable peak energy for some nuclei. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the scaling energies in Cd and Sn isotopes and a good centroid energy in Pb isotopes. A better description of ISGMR in Cd and Sn isotopes is achieved by the SkM* interaction, which has a somewhat softer value of the nuclear incompressibility.