${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ cluster resonances in ${}^{24}\mathrm{Mg}$ up to $E_x=50\text{MeV}$

The population and decay of excited states in ${}^{24}\mathrm{Mg}$ have been investigated using the ${}^{12}\mathrm{C}\left({}^{16}\mathrm{O},{}^{12}\mathrm{C}{}^{12}\mathrm{C}\right)\alpha$ reaction at beam energies of 135 and $160\text{MeV}$. This measurement permitted the decay spectrum to be measured up to ${}^{24}\mathrm{Mg}$ excitation energies of $70\text{MeV}$. Resonance structures were observed up to an excitation energy of $49.4\text{MeV}$ and spin $J=18\hslash$. The results are discussed in terms of the termination of a deformed ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ cluster band.

Figure 1

The total energy spectra for (a) the $135\text{MeV}$ measurement and (b) the $160\text{MeV}$ measurement.

Figure 2

(Color online) The Dalitz plot for the $160\text{MeV}$ experiment. The subscripts on ${{}^{12}\mathrm{C}}_{\left(i\right)}$ are particle labels. The upper panel displays the projection of the two dimensional spectrum onto the lower axis, and illustrates the contribution to the spectra from ${}^{16}\mathrm{O}$ excited states.

Figure 3

(Color online) A plot showing the calculated longitudinal momenta of the resonant ${}^{16}\mathrm{O}$ against transverse momentum.

Figure 4

The excitation energy spectra for the $135\text{MeV}$ experiment created for the $Q_{ggg}$, $Q_{gg}$, and $Q_g$ peaks.

Figure 5

The excitation energy spectra for the $160\text{MeV}$ experiment created for the $Q_{ggg}$, $Q_{gg}$, and $Q_g$ peaks.

Figure 6

The angular correlations for the peaks found in the $135\text{MeV}$ measurement. The curved lines show the Legendre polynomial matched with the data.

Figure 7

The angular correlations for the peaks found in the $160\text{MeV}$ measurement. The curved lines show the Legendre polynomial matched with the data.

Figure 8

The excitation energy spectra of Freer et al. [5] (a) compared with the excitation spectra from the $135\text{MeV}$ measurement (b) and the $160\text{MeV}$ measurement (c).

Figure 9

The excitation spectra taken from the $160\text{MeV}$ measurement are compared with the spectra of Freer et al. [5] in (a). (b) shows the spin systematics of both the present data with the data of Freer et al. The open circles, crosses, and plus signs correspond to tentative spin assignments from the data of Freer et al., the $135\text{MeV}$ measurement, and the $160\text{MeV}$ measurement, respectively. The filled circles, diamonds, and stars correspond to firm sign assignments from the data of Freer et al., the present $135\text{MeV}$ measurement, and the $160\text{MeV}$ measurement, respectively. The lines joining the points show that different spin assignments could be made for the same states in ${}^{24}\mathrm{Mg}$. The smaller circles at low excitation show known states at the Yrast line and the line is a best fit to these states.

Figure 10

A comparison between the excitation spectra of ${}^{24}\mathrm{Mg}$ from the (a) Cormier and Morsad resonances, and (b) the $160\text{MeV}$ measurement without the momentum cuts on the ${}^{16}\mathrm{O}^{*}$.