Anomaly in first-forbidden transitions of ¹⁷⁶Lu

¹⁷⁶Lu 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 T1/2 ≈ 3.7× 10¹⁰ years. The very long half-life is caused by two anomalous first-forbidden transitions from the 7⁻ state with extremely large comparative half-life logft ≈ 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 ¹⁷⁶Lu 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 T1/2 ≈ 1.95 × 10¹⁰ years.