Benford's Law and β-Decay Half-Lives

Abstract

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.