Full disassembly of excited ${}^{24}\mathrm{Mg}$ into six $\alpha$ particles

The decay of an excited ${}^{24}\mathrm{Mg}$ nucleus into six $\alpha$ particles is studied, from a selection of central ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reactions at 95 MeV beam energy, measured with the GARFIELD-RCo apparatus. Kinematic correlations among the detected $\alpha$ particles allow investigating the decay mechanism leading to the full disassembly of ${}^{24}\mathrm{Mg}$ into $\alpha$ particles. Experimental data indicate that the decay proceeds through intermediate doorway states involving excited states of ${}^{12}\mathrm{C}$ and ${}^8\mathrm{Be}$, with an important branching ratio estimated to be of the order of 40%. The possibility of a simultaneous breakup of the hot source in three bodies ($\alpha$, ${}^8\mathrm{Be}$, ${}^{12}\mathrm{C}$) is excluded in favor of a sequential emission. This is confirmed by comparison with statistical model predictions, where the emission of ${}^8\mathrm{Be}$ in both its ground state and first excited state is considered. Residual differences with respect to the statistical model are observed, particularly in the branching ratio of the Hoyle state with respect to higher excitation energy ${}^{12}\mathrm{C}$ states.

Figure 1

$E^{*}\left({}^{24}\mathrm{Mg}\right)$ distribution for original and reconstructed six-$\alpha$-particle events. Full points: data. Red line: $\mathrm{HF}\ell$ predictions. Blue dashed line: Gemini calculations. The arrow indicates what is expected from energy conservation.

Figure 2

Energy (upper) and angular (lower) distributions of $\alpha$ particles. Full points: data. Red line: $\mathrm{HF}\ell$ predictions. Blue dashed line: Gemini calculations.

Figure 3

Upper panels: excitation energy of a hypothetical intermediate ${}^{12}\mathrm{C}^{*}$ state calculated from the sum of the energies of the three $\alpha$ particles. (a) Black line: experimental data. Purple dashed line: $\mathrm{HF}\ell$ predictions treated like experimental data. (b) $\mathrm{HF}\ell$ predictions with (blue dashed) and without (black full) Be* emission. Lower panels: minimum $\alpha \text{−}\alpha$ relative energies for the group of $\alpha$ particles represented in the upper part: (c) experimental data; (d) $\mathrm{HF}\ell$ predictions with (blue dashed) and without (black full) Be* emission. The histograms are normalized to unitary area.

Figure 4

Minimum $\alpha \text{−}\alpha$ relative energies for the group of $\alpha$ particles not included in the ${}^{12}\mathrm{C}^{*}$ shown in Fig. 3. (a) experimental data (black line) and background estimated from the data with the event mixing technique (purple line). (b) $\mathrm{HF}\ell$ predictions with ${}^8\mathrm{Be}^{*}$ emission treated like experimental data (blue line) and background estimated from the predictions with the event mixing technique (purple line). (c) $\mathrm{HF}\ell$ predictions without ${}^8\mathrm{Be}^{*}$ emission with the decay channel $\left(i\right)$ (red dashed line) plotted separately from channels $\left(ii\right)$ to $\left(v\right)$ (black line). The histograms are normalized to unitary area.

Figure 5

Upper part: symmetrized Dalitz plot of the three intermediate-state fragments ($i,j,k={}^{12}\mathrm{C}^{*},{}^8\mathrm{Be}^{*},\alpha$). The coordinates are defined as $x=\sqrt{3}(E_i-E_j)/E_{\mathrm{tot}}$ and $y=(2E_k-E_i-E_j)/E_{\mathrm{tot}}$. Lower part: bidimensional plot of $\alpha \text{−}\alpha$ relative energy for the intermediate $({}^8\mathrm{Be},\alpha )$ system vs the $\alpha$-Be relative energy. Left panels show experimental data, while right panels give $\mathrm{HF}\ell$ predictions. For more details see text.

Figure 6

Topology of the three-body decay leading to vaporization. Upper part: distribution of $cos\left({\theta }_k\right)$; lower part: relative $\alpha$-Be energy. Left panels show experimental data, right panels show $\mathrm{HF}\ell$ predictions with (blue dashed lines) and without (black full lines) Be* emission. All the histograms have been normalized to unitary area.