Isoscalar giant monopole resonance within the Bohr-Mottelson model

Abstract

Background: With the possibility to measure the isoscalar giant monopole resonance (ISGMR) in the short-lived nuclei, the compressibility of the open-shell and exotic nuclei has attracted much attention.Purpose: The present work is an attempt to develop a semiclassical model to describe the ISGMR and the compressibility of the finite nuclei.Method: The fluid dynamical reduction of the Boltzmann-Langevin equation was carried out to describe the collective motion of the nucleus [Z. Phys. A 337, 413 (1990); Z. Phys. A 349, 119 (1994)]. In this work, by including the Skyrme energy density functional, we develop the model and apply it to the ISGMR. Both the self-consistent and linearized methods are used to solve the corresponding Langevin equation.Results: It is shown that the calculations of the ISGMR energies in this work agree with those by the relativistic mean-field theory and the random phase approximation, and reproduce the general trend of the data. The model only includes the two-body dissipation, and underestimates the width of the ISGMR. Twelve sets of the Skyrme interactions are applied to perform the calculations and study the incompressibility parameters in the leptodermous expansion. The calculated surface parameter ${K}_{S}$ within the model is smaller than the extracted value, and decreases linearly over mass number of the nucleus. The calculated values of the symmetry parameter ${K}_{\ensuremath{\tau}}$ and the Coulomb parameter ${K}_{C}$ agree with the extracted values by fitting the available data for the nuclei from $^{12}\mathrm{C}$ to $^{238}\mathrm{U}$.Conclusions: The Bohr-Mottelson model provides a reasonable method to understand the ISGMR in a macroscopic approach.