Investigation of the isoscalar response of ${}^{24}\mathrm{Mg}$ to ${}^6\mathrm{Li}$ scattering

Background: ${}^{24}\mathrm{Mg}$ is a strongly deformed nucleus in the ground state. Deformation effects can be observed in the structure of the isoscalar giant monopole and quadrupole resonances. ${}^{24}\mathrm{Mg}$ is also a nucleus that is well known to present different types of cluster-oscillation modes. Both giant resonances and cluster states are strongly populated by isoscalar transitions.

Purpose: To extract the $E0$, $E1$, and $E2$ transition strengths via ${}^6\mathrm{Li}$ scattering. The ${}^6\mathrm{Li}$ probe is a powerful tool for investigating the isoscalar nuclear response with a very favorable ratio of resonance-to-continuum background.

Method: Double-differential cross sections of ${}^6\mathrm{Li}$ inelastic scattering, at the beam energy of 100 MeV/u, were measured in the excitation-energy range $10\text{–}40\mathrm{MeV}$ and scattering angles $0-3{}^{\circ }$. A multipole-decomposition analysis was performed for extracting the isoscalar $E0$, $E1$, and $E2$ strength distributions.

Results: The extracted multipole strengths were compared with predictions from consistent quasiparticle random phase approximation calculations. The theoretical predictions are in fair agreement with the experimental data. The $E0$ strength was also compared with results from antisymmetrized molecular dynamics calculations found in the literature. A few peaks in the experimental data might be associated with clustering in ${}^{24}\mathrm{Mg}$.

Conclusions: Ground-state deformation effects were observed in the isoscalar giant monopole resonance (ISGMR) and isoscalar giant quadrupole resonance (ISGQR) distributions. The ISGMR strength is split in two peaks around 19 and 28 MeV. The ISGQR exhibits a pronounced peak at 20 MeV with a broadening at the low-energy region, similar to predictions from microscopic calculations. Signatures of excitation of cluster states were observed in the $E0$ response. Further studies including particle-decay measurements will be required to confirm the nature of the observed peaks.

Figure 1

On the top, angular distributions for the $({}^6\mathrm{Li},\stackrel{\prime }{{}^6\mathrm{Li}})$ reaction on ${}^{24}\mathrm{Mg}$ at different excitation energies. The experimental data were fitted with MDA using DWBA calculations for angular-momentum transfers of $\mathrm{\Delta }L=0-3$ (lines). On the bottom, double-differential cross sections for center-of-mass scattering angles at $0.{64}^{\circ }$, $1.{46}^{\circ }$, and $2.{28}^{\circ }$. The stacked histograms show the MDA results for monopole (red), dipole (blue), quadrupole (green), and higher order (yellow) contributions.

Figure 2

ISGMR strength function. (Top) The experimental data are compared with results from $\alpha$-scattering experiments of Refs. [23, 41] (bars). The data were fitted using a superposition of Lorentzian functions. (Bottom) Comparison with theoretical predictions from AMD [26] and fully consistent QRPA calculations. The QRPA distribution was shifted upward by 2 MeV.

Figure 3

ISGDR strength function. (Top) Same as Fig. 2. The data were fitted using a superposition of Lorentzian functions in the energy range from 10 to 26 MeV. (Bottom) Comparison with QRPA calculations showing the respective $0^{-}$ and $1^{-}$ components. The QRPA distributions were shifted upward by 2 MeV.

Figure 4

ISGQR strength function. (Top) Same as Fig. 2. (Bottom) Comparison with QRPA calculations showing the respective $K^{\pi }=$ $0^{+}$, $1^{+}$, and $2^{+}$ components. The QRPA distributions were shifted upward by 2 MeV.