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 quasi-particle 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=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 calculated peak energies and the strength distributions of ISGMR are compared with available experimental data. We find that SkP fails completely to describe the ISGMR strength distribution for all isotopes due to its low value of the nuclear matter incompressibility, namely K=202 MeV. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the ISGMR in Cd and Pb isotopes. A better description of ISGMR in Sn isotopes is achieved by the SkM* interaction, that has a somewhat softer value of the nuclear incompressibility.