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A unified formula for \(\alpha \) decay half-lives

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Abstract

Based on the Hatsukawa formula (Hatsukawa et al. in Phys Rev C 42:674, 1990), modifying the coefficient F(Z) and considering the blocking effect of unpaired nucleons, in our previous work (Xu and Liu in Eur Phys J A 58:16, 2022) we proposed an improved semi-empirical formula for evaluating the favored \(\alpha \) decay half-lives. In this work, considering the contribution of centrifugal potential, we generalize this formula to unfavored \(\alpha \) decay and propose a unified formula for \(\alpha \) decay half-lives. Using this formula, we systematically calculate the unfavored \(\alpha \) decay half-lives of 130 odd-A and 78 odd–odd nuclei with the corresponding root-mean-square (rms) deviations being 0.503 and 0.603, respectively. Meanwhile the rms deviation of \(\alpha \) decay half-lives for all the 700 nuclei taken from NUBASE2020 is only 0.380. Moreover, we extend this formula to predict the \(\alpha \) decay half-lives of 144 even–even, odd-A and odd–odd nuclei with Z = 117, 118, 119 and 120. For comparison, the unitary Royer formula (DZR) (Deng et al. in Phys Rev C 101:034307, 2020) proposed by Deng et al. and the modified universal decay law (MUDL) (Soylu and Qi in Nucl Phys A 1013:122221, 2021) proposed by Soylu et al. are also used. The predictions of these formulas are basically consistent with each other.

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Data Availability Statement

The manuscript has associated data in a data repository [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

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Acknowledgements

We would like to thank J. G. Deng, H. M. Liu, X. Pan, Y. T. Zou and H. F. Gui for useful discussion. This work is supported in part by the National Natural Science Foundation of China (Grants no. 12175100 and no. 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (Grant no. 21B0402 and no. 18A237), the Natural Science Foundation of Hunan Province, China (Grants no. 2018JJ2321), the Innovation Group of Nuclear and Particle Physics in USC, the Shandong Province Natural Science Foundation, China (Grant no. ZR2019YQ01) and the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment, University of South China (Grant no. 2019KFZ10).

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Authors and Affiliations

  1. School of Nuclear Science and Technology, University of South China, Hengyang, 421001, People’s Republic of China

    Yang-Yang Xu, De-Xing Zhu, Xun Chen & Xiao-Hua Li

  2. School of Math and Physics, University of South China, Hengyang, 421001, People’s Republic of China

    Xi-Jun Wu

  3. College of Physics and Electronics, Central South University, Changsha, 410083, People’s Republic of China

    Biao He

  4. National Exemplary Base for International Sci and Tech. Collaboration of Nuclear Energy and Nuclear Safety, University of South China, Hengyang, 421001, People’s Republic of China

    Xiao-Hua Li

  5. Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment, University of South China, Hengyang, 421001, People’s Republic of China

    Xiao-Hua Li

  6. Key Laboratory of Low Dimensional Quantum Structures and Quantum Control, Hunan Normal University, 410081, Changsha, People’s Republic of China

    Xiao-Hua Li

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  1. Yang-Yang Xu
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Xu, YY., Zhu, DX., Chen, X. et al. A unified formula for \(\alpha \) decay half-lives. Eur. Phys. J. A 58, 163 (2022). https://doi.org/10.1140/epja/s10050-022-00812-9

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