Microscopic Study of the Isoscalar Giant Monopole Resonance in Cd, Sn and Pb Isotopes

TL;DR

This study investigates the isoscalar giant monopole resonance in Cd, Sn, and Pb isotopes using Skyrme Hartree-Fock+BCS and QRPA models, comparing different parameter sets and pairing forces to experimental data.

Contribution

It systematically analyzes the impact of various Skyrme parameter sets and pairing interactions on ISGMR predictions in multiple isotopes.

Findings

SkP fails to describe ISGMR due to low incompressibility

SLy5 provides reasonable ISGMR description for Cd and Pb

SkM* yields better results for Sn isotopes

Abstract

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.