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arXiv · 2303.08332

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

W. Horiuchi·T. Sato·Y. Uesaka·K. Yoshida
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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\%.

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W. Horiuchi, T. Sato, Y. Uesaka, K. Yoshida. 2023-03-15. Electron wave functions in beta-decay formulas revisited (II): Completion including recoil-order and induced currents. https://doi.org/10.1093/ptep%2Fptad089

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