Isoscalar giant monopole resonance in $^{24}$Mg and $^{28}$Si: Effect of coupling between the isoscalar monopole and quadrupole strength

TL;DR

This paper investigates the coupling effects between isoscalar giant monopole and quadrupole resonances in deformed nuclei $^{24}$Mg and $^{28}$Si, using experimental alpha scattering data and QRPA calculations to understand nuclear incompressibility.

Contribution

It provides a detailed analysis of the two-peaked ISGMR structure in deformed nuclei and identifies the Skyrme functional that best matches experimental data, enhancing understanding of nuclear incompressibility.

Findings

Identification of the two-peak structure in ISGMR due to deformation and coupling.

Determination of the Skyrme functional that best reproduces experimental data.

Insights into the deformation splitting of the ISGQR in deformed nuclei.

Abstract

Background: In highly deformed nuclei, there is a noticeable coupling of the Isoscalar Giant Monopole Resonance (ISGMR) and the $K = 0$ component of the Isoscalar Giant Quadrupole Resonance (ISGQR), which results in a double peak structure of the isoscalar monopole (IS0) strength (a narrow low-energy deformation-induced peak and a main broad ISGMR part). The energy of the narrow low-lying IS0 peak is sensitive to both the incompressibility modulus $K_\infty$ and the coupling between IS0 and isoscalar quadrupole (IS2) strength. Objective: This study aims to investigate the two-peaked structure of the ISGMR in the prolate $^{24}$Mg and oblate $^{28}$Si nuclei and identify among a variety of energy density functionals based on Skyrme parameterisations the one which best describes the experimental data. This will allow for conclusions regarding the nuclear incompressibility. Because of the strong IS0/IS2 coupling, the deformation splitting of the ISGQR will also be analysed. Methods: The ISGMR was excited in $^{24}$Mg and $^{28}$Si using $\alpha$-particle inelastic scattering measurements acquired with an $E_\alpha = 196$ MeV beam at scattering angles $\theta_{\text{Lab}} = 0^\circ$ and $4^\circ$. The K$600$ magnetic spectrometer at iThemba LABS was used to detect and momentum analyse the inelastically scattered $\alpha$ particles. An experimental energy resolution of $\approx 70$ keV (FWHM) was attained, revealing fine structure in the excitation-energy region of the ISGMR. The IS0 strength distributions in the nuclei studied were obtained with the Difference-of-Spectrum (DoS) technique. The theoretical comparison is based on the quasiparticle random-phase approximation (QRPA) with a representative set of Skyrme forces.