The 3$α$ correlations of ground and excited $0^+$ states of $^{12}\mathrm{C}$ within the microscopic cluster model
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| Format: | Preprint |
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2025
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| _version_ | 1866915109773770752 |
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| author | Tao, De-Ye Zhou, Bo Ma, Yu-Gang |
| author_facet | Tao, De-Ye Zhou, Bo Ma, Yu-Gang |
| contents | 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 $3α$ correlations without assuming the existence of $^8\mathrm{Be}$. In particular, the key quantity -- two-cluster overlap amplitudes -- is calculated for the $3α$ 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 ($0S$) configuration, while the $0_3^+$ state shows a more extended $3α$ clustering structure, which can be viewed as a breathing-like excitation of the Hoyle state, with an additional nodal structure. 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 $2α$ correlation in the $D\otimes D$ channel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The 3$α$ correlations of ground and excited $0^+$ states of $^{12}\mathrm{C}$ within the microscopic cluster model Tao, De-Ye Zhou, Bo Ma, Yu-Gang Nuclear Theory 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 $3α$ correlations without assuming the existence of $^8\mathrm{Be}$. In particular, the key quantity -- two-cluster overlap amplitudes -- is calculated for the $3α$ 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 ($0S$) configuration, while the $0_3^+$ state shows a more extended $3α$ clustering structure, which can be viewed as a breathing-like excitation of the Hoyle state, with an additional nodal structure. 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 $2α$ correlation in the $D\otimes D$ channel. |
| title | The 3$α$ correlations of ground and excited $0^+$ states of $^{12}\mathrm{C}$ within the microscopic cluster model |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2501.10664 |