The European Physical Journal A

, Volume 38, Issue 3, pp 251–255 | Cite as

Benford’s law and half-lives of unstable nuclei

  • Dongdong NiEmail author
  • Zhongzhou Ren
Regular Article - Theoretical Physics


We find that the experimental data of the \( \alpha\) -decay half-lives for 627 nuclei are in good agreement with Benford’s law, which states that the frequency of the appearance of each figure, 1-9, as the first significant digit, follows a logarithmic distribution favoring the smallest value. In order to generalize the applicability of Benford’s law, we systematically investigate the data of the total half-lives for 3177 nuclides in their ground and isomeric states, where the half-lives of many nuclei are determined by \( \beta\) -decay and spontaneous fission. We find that they are also in excellent agreement with Benford’s law, although they are determined by different interactions such as strong, weak and electromagnetic interactions. The possible physics behind them is discussed. Moreover, Benford’s law can be used to test theoretical models or methods.


02.50.Cw Probability theory 21.10.-k Properties of nuclei; nuclear energy levels 21.10.Tg Lifetimes, widths 23.60.+e \( \alpha\) decay 


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Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.Department of PhysicsNanjing UniversityNanjingPRC
  2. 2.Center of Theoretical Nuclear PhysicsNational Laboratory of Heavy-Ion AcceleratorLanzhouPRC
  3. 3.Kavli Institute for Theoretical Physics ChinaBeijingPRC

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