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Electron wave functions in beta-decay formulas revisited (I) : Gamow-Teller and spin-dipole contributions to allowed and first-forbidden transitions
| Title: | Electron wave functions in beta-decay formulas revisited (I) : Gamow-Teller and spin-dipole contributions to allowed and first-forbidden transitions |
| Authors: | Horiuchi, Wataru Browse this author →KAKEN DB | | Sato, Toru Browse this author | | Uesaka, Yuichi Browse this author | | Yoshida, Kenichi Browse this author |
| Issue Date: | 2022 |
| Publisher: | Oxford University Press |
| Journal Title: | Progress of theoretical and experimental physics |
| Volume: | 2021 |
| Issue: | 10 |
| Start Page: | 103D03 |
| Publisher DOI: | 10.1093/ptep/ptab069 |
| 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 are linear to the radius for the s-wave andp-wave wave functions, respectively. We find, however, that 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. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/84399 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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