Isoscalar monopole and dipole transitions in ${}^{24}$Mg, ${}^{26}$Mg and ${}^{28}$Si

Abstract

Nuclei in the $sd$-shell demonstrate a remarkable interplay of cluster and mean-field phenomena. The $N=Z$ nuclei, such as ${}^{24}$Mg and ${}^{28}$Si, have been the focus of the theoretical study of both these phenomena in the past. The cluster and vortical mean-field phenomena can be probed by excitation of isoscalar monopole and dipole states in scattering of isoscalar particles such as deuterons or $\alpha$ particles. Inelastically scattered $\alpha$ particles were momentum-analysed in the K600 magnetic spectrometer at iThemba LABS, Cape Town, South Africa. The scattered particles were detected in two multi-wire drift chambers and two plastic scintillators placed at the focal plane of the K600. In the theoretical discussion, the QRPA and AMD+GCM were used. The QRPA calculations lead us to conclude that: i) the mean-field vorticity appears mainly in dipole states with $K=1$, ii) the dipole (monopole) states should have strong deformation-induced octupole (quadrupole) admixtures, and iii) that near the $\alpha$-particle threshold, there should exist a collective state (with $K=0$ for prolate nuclei and $K=1$ for oblate nuclei) with an impressive octupole strength. The results of the AMD+GCM calculations suggest that some observed states may have a mixed (mean-field + cluster) character or correspond to particular cluster configurations. A tentative correspondence between observed states and theoretical states from QRPA and AMD+GCM was established. The QRPA and AMD+GCM analysis shows that low-energy isoscalar dipole states combine cluster and mean-field properties. The QRPA calculations show that the low-energy vorticity is well localized in ${}^{24}$Mg, fragmented in ${}^{26}$Mg, and absent in ${}^{28}$Si.

11 figures, 18ish pages, accepted in Phys Rev C

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• $\alpha$-cluster decay from ${}^{24}$Mg resonances produced in ${}^{12}$C(${}^{16}$O,${}^{24}$Mg)$\alpha$ reaction
• Symmetry-restored Skyrme-Random-Phase-Approximation calculations of the monopole strength in deformed nuclei
• The 2025 Evaluation of Experimental Thermonuclear Reaction Rates (ETR25)