Non-characteristic Half-lives in Radioactive Decay

TL;DR

This paper analyzes the distribution of radioactive half-lives, finds a consistent power-law with an exponent around 1.1, and introduces a new mechanism explaining this pattern based on decay energy relationships.

Contribution

It demonstrates the existence of a power-law distribution in half-lives and proposes a novel energy-based mechanism for its generation, challenging previous goodness-of-fit methods.

Findings

Half-lives follow a power-law distribution with an exponent around 1.1.

Existing fitting procedures may not accurately identify power-laws in this context.

A new energy-based mechanism explains the power-law generation in alpha decay.

Abstract

Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that explore a method for fitting power-laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation.