Isoscalar giant monopole resonance in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Mg</mml:mi><mml:mprescripts /><mml:none /><mml:mn>24</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Si</mml:mi><mml:mprescripts /><mml:none /><mml:mn>28</mml:mn></mml:mmultiscripts></mml:math> : Effect of coupling between the isoscalar monopole and quadrupole strength

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