{
  "id": "2303.08332",
  "version": "v1",
  "published": "2023-03-15T02:40:57.000Z",
  "updated": "2023-03-15T02:40:57.000Z",
  "title": "Electron wave functions in beta-decay formulas revisited (II): Completion including recoil-order and induced currents",
  "authors": [
    "W. Horiuchi",
    "T. Sato",
    "Y. Uesaka",
    "K. Yoshida"
  ],
  "comment": "25 pages, 2 figures",
  "categories": [
    "nucl-th"
  ],
  "abstract": "We present complete formulas of the allowed and first-forbidden transitions of the nuclear beta decay taking into account the recoil-order and induced currents up to the next-to-leading order (NLO). The longitudinal part of the vector current is cleared away by the use of the conservation of the vector current for the multipole operators of the natural-parity transitions, which makes the effect of the meson exchange current for the vector current as small as possible. The formula is transparent enough to be applied to various beta-decay processes. As a numerical demonstration, we apply our formulas to the beta decay of a neutron-rich nucleus $^{160}$Sn. We find that the NLO corrections amount to 10--20\\% of the total decay rate, whereas the induced currents alter the rate at most 5\\%.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-15T02:40:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "electron wave functions",
      "induced currents",
      "beta-decay formulas",
      "vector current",
      "recoil-order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}