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- 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; Sato, Toru; Uesaka, Yuichi; Yoshida, Kenichi
- 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 and |$p$| -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.
- Subjects
LEPTON-hadron scattering; ENERGY level densities; APPROXIMATION theory; DIRAC equation; ELECTRON beams
- Publication
Progress of Theoretical & Experimental Physics: PTEP, 2021, Vol 2021, Issue 10, p1
- ISSN
2050-3911
- Publication type
Article
- DOI
10.1093/ptep/ptab069