Wavelet analysis of monopole strength in highly deformed $^{24}$Mg

TL;DR

This study analyzes monopole excitations in the highly deformed nucleus Mg-24 using a fully self-consistent QRPA framework with SkPδ and SVbas. Wavelet analysis of high-resolution inelastic alpha scattering data reveals that deformation-induced MQC dominates the fine structure in the 10–18 MeV range, while the ISGMR lies at higher energies; the observed energy scales are broad (roughly 200 keV to 1–2 MeV). The residual interaction, i.e., Landau damping, is essential to reproduce realistic wavelet powers and scales, and deformation softness further improves agreement with experiment. The work highlights the importance of including MQC and deformation effects in describing the monopole response of deformed light nuclei, and suggests that coupling to more complex configurations may be needed for complete quantitative consistency.

Abstract

Experimental data on $α$-particle inelastic scattering for monopole excitations in $^{24}$Mg in the excitation-energy region $E_{\rm 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 SkP$^δ$ force, which corresponds to a low nuclear incompressibility of $K_{\infty}$$=$$202$ MeV. Extraction of energy scales, by means of wavelet analysis, characterizing the observed fine structure 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. Characteristic energy scales are extracted from the fine structure using continuous wavelet transforms. The experimental results are compared to QRPA calculations employing the Skyrme parameterizations SkP$^δ$ and SVbas. 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 (2qp) monopole strengths are compared. The results demonstrate that the residual interaction plays a key role in reproducing realistic wavelet powers and characteristic energy scales. Overall, a continuous range of scales $δE$$=$$200$$-$$1000$ keV is obtained rather than distinct isolated scales. The deformation softness of $^{24}$Mg is found to significantly influence both the monopole strength distribution and the wavelet characteristics.

Figures (7)

• Figure 1: The calculated potential energy surface (PES) as a function of the axial quadrupole deformation $\beta$.
• Figure 2: The monopole (top) and quadrupole (bottom) strength functions calculated with SkP$^\delta$ (left) and SVbas (right) forces.
• Figure 3: Left column: Experimental isoscalar monopole strength distribution in $^{24}$Mg compared with QRPA model predictions folded with the experimental energy resolution ($\Delta E$$=$$70~\text{keV}$). Middle column: Real parts of the corresponding wavelet transforms, $\mathrm{Re}[C(\delta E, E_\text{x})]$. Right column: Moduli of the wavelet transforms, $|C(\delta E, E_\text{x})|$. Vertical dashed lines indicate the excitation-energy intervals ($10$$-$$24$ MeV, $10$$-$$18$ MeV and $18$$-$$24$ MeV) over which the wavelet coefficients are summed to obtain the power spectra displayed in Fig. \ref{['powers']}.
• Figure 4: Experimental (top) and theoretical QRPA power spectra calculated with the SkP$^{\delta}$ (middle, including the deformation-averaged strength function shown in the lowest row) and SVbas (bottom) interactions for $^{24}$Mg. Results are shown for the total excitation-energy range $10$$–$$24$ MeV (left), the MQC region $10$$–$$18$ MeV (middle), and the ISGMR region $18$$–$$24$ MeV (right). Energy scales and their associated errors are indicated by filled circles and horizontal bars, respectively. In the experimental panels (top), the additional vertical gray bars denote the $1\sigma$ statistical errors; the same gray bars are reproduced in the theoretical panels for direct comparison.
• Figure 5: Non-normalized SkP$^\delta$ (top) and SVbas (bottom) powers for MQC ($10$$-$$18$ MeV) and ISGMR ($18$$-$$24$ MeV) energy ranges.