{
  "id": "2303.17777",
  "version": "v1",
  "published": "2023-03-31T02:49:02.000Z",
  "updated": "2023-03-31T02:49:02.000Z",
  "title": "$α$ + $^{92}$Zr cluster structure in $^{96}$Mo",
  "authors": [
    "S. Ohkubo",
    "Y. Hirabayashi"
  ],
  "comment": "11 pages, 9 figures",
  "journal": "Physical Review C 2023 March issue",
  "doi": "10.1103/PhysRevC.107.034317",
  "categories": [
    "nucl-th"
  ],
  "abstract": "In the evaluation of the half-life of the neutrinoless double-$\\beta$ decay ($0\\nu\\beta\\beta$) of a doubly closed-subshell nucleus $^{96}$Zr, the structure of the nucleus $^{96}$Mo is essentially important. The $\\alpha$-clustering aspects of $^{96}$Mo are investigated for the first time. By studying the nuclear rainbows in $\\alpha$ scattering from $^{92}$Zr at high energies and the characteristic structure of the excitation functions at the extreme backward angle at the low-energy region, the interaction potential between the $\\alpha$ particle and the $^{92}$Zr nucleus is determined well in the double folding model. The validity of the double folding model was reinforced by studying $\\alpha$ scattering from neighboring nuclei $^{90}$Zr, $^{91}$Zr, and $^{94}$Zr. The double-folding-model calculations reproduced well all the observed angular distributions over a wide range of incident energies and the characteristic excitation functions. By using the obtained potential the $\\alpha$ +$^{92}$Zr cluster structure of $^{96}$Mo is investigated in the spirit of a unified description of scattering and structure. The existence of the second-higher nodal band states with the $\\alpha$+ $^{92}$Zr cluster structure, in which two more nodes are excited in the relative motion compared with the ground band, is demonstrated. The calculation reproduces well the ground-band states of $^{96}$Mo in agreement with experiment. The experimental $B(E2)$ value of the transition in the ground band is also reproduced well. The effect of $\\alpha$ clustering in $^{96}$Mo on the the half-life of the $0\\nu\\beta\\beta$ double-$\\beta$ decay of $^{96}$Zr is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-31T02:49:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zr cluster structure",
      "ground band",
      "second-higher nodal band states",
      "double folding model",
      "characteristic excitation functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. C"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}