{
  "id": "2501.10664",
  "version": "v1",
  "published": "2025-01-18T06:07:11.000Z",
  "updated": "2025-01-18T06:07:11.000Z",
  "title": "The 3$α$ correlations of ground and excited $0^+$ states of $^{12}\\mathrm{C}$ within the microscopic cluster model",
  "authors": [
    "De-Ye Tao",
    "Bo Zhou",
    "Yu-Gang Ma"
  ],
  "comment": "6 pages, 3 figures",
  "categories": [
    "nucl-th"
  ],
  "abstract": "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 the $3\\alpha$ 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 ($0S$) configuration, while the $0_3^+$ state shows a more extended $3\\alpha$ 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 $2\\alpha$ correlation in the $D\\otimes D$ channel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-18T06:07:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "microscopic cluster model",
      "hoyle state",
      "correlation",
      "ground state",
      "additional nodal structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}