{
  "id": "1607.02832",
  "version": "v1",
  "published": "2016-07-11T06:36:44.000Z",
  "updated": "2016-07-11T06:36:44.000Z",
  "title": "Hoyle family and linear-chain state in 12C",
  "authors": [
    "Yasuro Funaki"
  ],
  "comment": "8 pages, 8 figures, 1 table",
  "categories": [
    "nucl-th",
    "nucl-ex"
  ],
  "abstract": "Background: Two new $J^\\pi=0^+$ states are recently observed around a few MeV above the Hoyle state (the second $0^+$ state in 12C). The characters of them are only poorly discussed in theory and are still mysterious. Purpose: I give for the first time a comprehensive understanding of the structures of the $0^+$ states by analyzing their wave functions, and discuss relationship with the Hoyle state, similarities, and differences between the states. Method: I extend a microscopic $\\alpha$-cluster model called Tohsaki-Horiuchi-Schuck-R\\\"opke (THSR) wave function so as to incorporate $2\\alpha+\\alpha$ asymmetric configuration explicitly. The so-called $r^2$-constraint method to effectively eliminate spurious continuum components is also used. Results: The $0_3^+$ state is shown to have a very large squared overlap with a single configuration of the extended THSR wave function in an orthogonal space to the Hoyle state as well as to the ground state. The $0_4^+$ state has a maximal squared overlap with a single extended THSR wave function with an extremely prolately-deformed shape. Conclusions: The $0_3^+$ state appears as a family of the Hoyle state to have a higher nodal structure in the internal motions of the $3\\alpha$ clusters, due to the orthogonalization to the Hoyle state. The $0_4^+$ state dominantly has a linear-chain structure, where the $3\\alpha$ clusters move freely in a non-localized way, like a one-dimensional gas of the $3\\alpha$ clusters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-11T06:36:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hoyle state",
      "linear-chain state",
      "hoyle family",
      "single extended thsr wave function",
      "effectively eliminate spurious continuum components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}