{
  "id": "2103.16815",
  "version": "v1",
  "published": "2021-03-31T05:19:13.000Z",
  "updated": "2021-03-31T05:19:13.000Z",
  "title": "Beta-decay formulas revisited (I): Gamow--Teller and spin-dipole contributions to allowed and first-forbidden transitions",
  "authors": [
    "W. Horiuchi",
    "T. Sato",
    "Y. Uesaka",
    "K. Yoshida"
  ],
  "comment": "28 pages, 8 figures",
  "categories": [
    "nucl-th",
    "hep-ph"
  ],
  "abstract": "We propose formulas of the nuclear beta-decay rate that are useful in a practical calculation. The decay rate is determined by the product of the lepton and hadron current densities. A widely used formula relies upon the fact that the low-energy lepton wave functions in a nucleus can be well approximated by a constant and linear to the radius for the $s$-wave and $p$-wave wave functions, respectively. We find, however, the deviation from such a simple approximation is evident for heavy nuclei with large $Z$ by numerically solving the Dirac equation. In our proposed formulas, the neutrino wave function is treated exactly as a plane wave, while the electron wave function is obtained by iteratively solving the integral equation, thus we can control the uncertainty of the approximate wave function. The leading-order approximation gives a formula equivalent to the conventional one and overestimates the decay rate. We demonstrate that the next-to-leading-order formula reproduces well the exact result for a schematic transition density as well as a microscopic one obtained by a nuclear energy-density functional method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-31T05:19:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spin-dipole contributions",
      "beta-decay formulas",
      "first-forbidden transitions",
      "nuclear energy-density functional method",
      "gamow-teller"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}