{
  "id": "1503.04261",
  "version": "v1",
  "published": "2015-03-14T02:55:29.000Z",
  "updated": "2015-03-14T02:55:29.000Z",
  "title": "Alpha cluster structures and monopole excitations in $^{13}$C",
  "authors": [
    "Taiichi Yamada",
    "Yasuro Funaki"
  ],
  "comment": "9 figures",
  "categories": [
    "nucl-th",
    "nucl-ex"
  ],
  "abstract": "The structure of $1/2^{\\pm}$ states in $^{13}$C up to around the $3\\alpha+n$ threshold ($E_x = 12.3$~MeV) is investigated with a full four-body $3\\alpha+n$ orthogonality condition model (OCM) calculation, where the $3\\alpha$ OCM, the model space of which is the subspace of the $3\\alpha+n$ model, describes well the structure of the low-lying states of $^{12}$C including the $2^{+}_2$, $0^{+}_3$, and $0^{+}_4$ states, which have been recently observed above the Hoyle state ($0^+_2$). A full spectrum up to the $1/2^{-}_5$ ($1/2^{+}_3$) state is reproduced consistently with the lowest five $1/2^{-}$ (three $1/2^{+}$) states of experimental spectrum. It is shown that the $1/2^{-}_2$ and $1/2^{-}_3$ states are characterized by the dominant cluster configurations of $^{9}$Be($3/2^-$,$1/2^-$)+$\\alpha$, while the ground state $1/2^-_1$ has a shell-model-like structure. The calculated monopole transition strengths to the $1/2^{-}_{2,3}$ states are consistent with the experimental data, although the shell model calculations have a difficulty to reproduce them. These results indicate that the excited $1/2^-$ states have cluster structures. On the other hand, the $1/2^{+}_{1}$ state is found to have a loosely bound neutron structure in which the extra neutron moves around $^{12}$C(g.s) core with $1S$ orbit, reflecting the fact that this state appears by $1.9$~MeV just below the $^{12}$C(g.s)+$n$ threshold, while the $1/2^{+}_{2}$ and $1/2^{+}_{3}$ states are characterized by $^{9}$Be+$\\alpha$ structures. We found that the $1/2^+_5$ state located above the $3\\alpha+n$ threshold is the Hoyle analogue state in $^{13}$C, the wave function of which is described by product states of constituent clusters, $(0S)^3_{\\alpha}(S)_n$, with the probability of $52~\\%$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-14T02:55:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "21.10.Dr",
      "21.10.Gv",
      "21.60.Gx",
      "03.75.Hh"
    ],
    "keywords": [
      "alpha cluster structures",
      "monopole excitations",
      "hoyle analogue state",
      "orthogonality condition model",
      "dominant cluster configurations"
    ],
    "publication": {
      "doi": "10.1103/PhysRevC.92.034326"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1352867
    }
  }
}