Benford's Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford's law, which states that the frequency of occurrence of each figure, 1-9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford's logarithmic distribution of β-decay half-lives can be explained in terms of Newcomb's justification of Benford's law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford's law. This indicates that Benford's law is useful for theoretical physicists to test their methods for calculating β-decay half-lives. (nuclear physics)