{
  "id": "1808.05016",
  "version": "v1",
  "published": "2018-08-15T09:49:27.000Z",
  "updated": "2018-08-15T09:49:27.000Z",
  "title": "$0νββ$ nuclear matrix elements, neutrino potentials and $\\mathrm{SU}(4)$ symmetry",
  "authors": [
    "Fedor Šimkovic",
    "Adam Smetana",
    "Petr Vogel"
  ],
  "comment": "12 pages, 9 figures",
  "categories": [
    "nucl-th"
  ],
  "abstract": "Intimate relation between the Gamow-Teller part of the matrix element $M^{0\\nu}_\\mathrm{GT}$ and the $2\\nu\\beta\\beta$ closure matrix element $M^{2\\nu}_\\mathrm{cl}$ is explained and explored. If the corresponding radial dependence $C^{2\\nu}_\\mathrm{cl}(r)$ would be known, $M^{0\\nu}$ corresponding to any mechanism responsible for the $0\\nu\\beta\\beta$ decay can be obtained as a simple integral. However, the $M^{2\\nu}_\\mathrm{cl}$ values sensitively depend on the properties of higher lying $1^+$ states in the intermediate odd-odd nuclei. We show that the $\\beta^-$ and $\\beta^+$ amplitudes of such states typically have opposite relative signs, and their contributions reduce severally the $M^{2\\nu}_\\mathrm{cl}$ values. Vanishing values of $M^{2\\nu}_\\mathrm{cl}$ are signs of a partial restoration of the spin-isospin $\\mathrm{SU}(4)$ symmetry. We suggest that demanding that $M^{2\\nu}_\\mathrm{cl}$ = 0 is a sensible way, within the method of the Quasi-particle Random Phase Approximation (QRPA), of determining the amount of renormalization of isoscalar particle-particle interaction strength $g^{T=0}_{pp}$. Using such prescription, the matrix elements $M^{0\\nu}$ are evaluated; their values are not very different ($\\le$ 20\\%) from the usual QRPA values when $g^{T=0}_{pp}$ is related to the known $2\\nu\\beta\\beta$ half-lives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-15T09:49:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nuclear matrix elements",
      "neutrino potentials",
      "quasi-particle random phase approximation",
      "isoscalar particle-particle interaction strength",
      "closure matrix element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}