The cluster structures of the $0^{+}$ states in ${}^{12}\mathrm{C}$, including the ground state, the Hoyle state, and the recently identified $0_3^{+}$ and $0_4^{+}$ states, are analyzed to explore the cluster configurations and $3\alpha$ correlations without assuming the existence of ${}^8\mathrm{Be}$. In particular, the key quantity—two-cluster overlap amplitudes—is calculated for $3\alpha$ clustering channels to reveal the essential features of these $0^{+}$ states. The results clearly show the distinction between the compact structure of the ground state and the gas-like structures of the excited $0^{+}$ states. The Hoyle state exhibits the expected gas-like dominant $\left(0S\right)$ configuration, while the $0_3^{+}$ state shows a more extended $3\alpha$ clustering structure, which can be viewed as a breathing-mode excitation of the Hoyle state. The $0_4^{+}$ state is found to have a mixed configuration, featuring a bent-arm-like structure in the $S\otimes S$ channel and an enhanced $2\alpha$ correlation in the $D\otimes D$ channel.

Close

PrevNext

View figure in article

• Cluster models
• 6 ≤ A ≤ 19
• Nuclear structure & decays