Electron wave functions in beta-decay formulas revisited (II): Completion including recoil-order and induced currents

• Published in: Progress of theoretical and experimental physics Vol. 2023; no. 7
• Main Authors: Horiuchi, Wataru, Sato, Toru, Uesaka, Yuichi, Yoshida, Kenichi
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.07.2023
• Subjects: Approximation; Gravitational waves; Neutrinos; Nuclear physics
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptad089

We present complete formulas of the allowed and first-forbidden transitions of 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 160Sn. We find that the NLO corrections amount to 10–20 percent of the total decay rate, whereas the induced currents alter the rate at most by 5 percent.