Monopole giant resonance in $^{100-132}$Sn, $^{144}$Sm and $^{208}$Pb

TL;DR

This study investigates the isoscalar giant monopole resonance in various spherical nuclei using Skyrme RPA, revealing challenges in simultaneously describing GMR across different nuclei and highlighting the role of effective mass.

Contribution

It demonstrates that current Skyrme forces cannot uniformly describe GMR in Sn, Sm, and Pb nuclei, and suggests the isoscalar effective mass influences GMR peak energies.

Findings

Different incompressibility values are needed for Sn and heavier nuclei.

GMR peak energy in $^{120}$Sn depends on the isoscalar effective mass.

Current Skyrme forces cannot simultaneously fit GMR data in all studied nuclei.

Abstract

The isoscalar giant monopole resonance (GMR) in spherical nuclei $^{100-132}$Sn, $^{144}$Sm, and $^{208}$Pb is investigated within the Skyrme random-phase-approximation (RPA) for a variety of Skyrme forces and different pairing options. The calculated GMR strength functions are directly compared to the available experimental distributions. It is shown that, in accordance to results of other groups, description of GMR in Sn and heavier Sm/Pb nuclei needs different values of the nuclear incompressibilty, $K \approx$ 200 or 230 MeV, respectively. Thus none from the used Skyrme forces is able to describe GMR in these nuclei simultaneously. The GMR peak energy in open-shell $^{120}$Sn is found to depend on the isoscalar effective mass, which might be partly used for a solution of the above problem. Some important aspects of the problem (discrepancies of available experimental data, proper treatment of the volume and surface compression in finite nuclei, etc) are briefly discussed.