Background: Experimental data on $\alpha$-particle inelastic scattering for monopole excitations in ${}^{24}\mathrm{Mg}$ in the excitation-energy region $E_{\mathrm{x}}=9–25$ MeV, obtained at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS), have been analyzed within a fully self-consistent quasiparticle random-phase approximation (QRPA) framework using two Skyrme parametrizations. A good overall agreement with the experimental data is achieved, particularly with the ${\mathrm{SkP}}^{\delta }$ force, which corresponds to a low nuclear incompressibility of $K_{\infty }=202$ MeV.

Purpose: To extract energy scales, by means of wavelet analysis, characterizing the observed fine structure in the main peak of the isoscalar giant monopole resonance (ISGMR) as well as the low-energy region 10–18 MeV of the deformation-induced monopole-quadrupole coupling (MQC) in order to investigate the damping mechanism contributing to their decay widths.

Methods: Characteristic energy scales and power spectra are extracted from the fine structure using continuous wavelet transforms. The experimental results are compared to QRPA calculations employing the Skyrme parametrizations ${\mathrm{SkP}}^{\delta }$ and SVbas.

Results: A significant, if not decisive, impact of the MQC strength on the wavelet power spectra is observed across the entire excitation-energy range of 10–24 MeV. Wavelet features derived from the QRPA and from unperturbed two-quasiparticle monopole strengths are compared. The results demonstrate that the residual interaction plays a key role in reproducing wavelet powers and characteristic energy scales. Overall, a continuous range of scales $\delta E=200–1000$ keV is obtained rather than distinct isolated scales. The deformation softness of ${}^{24}\mathrm{Mg}$ is found to significantly influence both the monopole strength distribution and the wavelet characteristics.

Conclusions: Similar to the case of the isovector giant dipole resonance, the dominant role of Landau damping is confirmed as the main decay mechanism of the ISGMR in the highly deformed nucleus ${}^{24}\mathrm{Mg}$. At the same time, the remaining discrepancies between experiment and theory highlight the possible importance of couplings to more complex configurations.

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• H & He induced nuclear reactions
• Inelastic scattering reactions
• Nuclear structure & decays
• Spectroscopic factors & electromagnetic moments
• 20 ≤ A ≤ 38
• Spectrometers & spectroscopic techniques