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arXiv · 2509.24549

Anomaly in first-forbidden transitions of $^{176}$Lu

Jing-Wen Ran·Long-Jun Wang
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Abstract

$^{176}$Lu is the key nucleus for understanding the evolution of planetary bodies in the solar system, and the temperature and nucleosynthesis of the $s$ process, due to its very long terrestrial half-life $T_{1/2} \approx 3.7\times 10^{10}$ years. The very long half-life is caused by two anomalous first-forbidden transitions from the $7^-$ state with extremely large comparative half-life log$ft \approx 19$ which have never been appeared in other cases of the existing nuclear databases. We analyze the underlying mechanism and reason for the anomaly in first-forbidden transitions of $^{176}$Lu for the first time, which is based on the projected shell model. It is found that the possible $K$-forbidden nature is indispensable for describing the two extremely weak first-forbidden transitions, and the transition strengths are very sensitive to the detailed configuration mixing and $K$ mixing in the nuclear wave functions. The half-life of the $7^-$ state is calculated to be $T_{1/2} \approx 1.95 \times 10^{10}$ years.

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Jing-Wen Ran, Long-Jun Wang. 2025-09-29. Anomaly in first-forbidden transitions of $^{176}$Lu. https://arxiv.org/abs/2509.24549

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