Noncharacteristic half-lives in radioactive decay

Area of Science:

• Nuclear Physics
• Statistical Analysis
• Radiochemistry

Background:

• Radionuclide half-lives exhibit an exceptionally wide range, spanning over 50 orders of magnitude.
• Understanding the probability distribution of these half-lives is crucial for nuclear science and applications.

Purpose of the Study:

• To characterize the probability distribution of radionuclide half-lives.
• To evaluate existing methods for fitting power laws and assessing goodness-of-fit.
• To identify and explain the underlying physical mechanisms generating observed distributions.

Main Methods:

• Analysis of a comprehensive dataset of radionuclide half-lives.
• Application and critique of statistical methods for power-law fitting and goodness-of-fit testing, including the Clauset et al. (2009) procedure.
• Correlation analysis between half-life, decay rate, and released energy for various disintegration types.

Main Results:

• The Clauset et al. (2009) method was found to perform poorly, incorrectly rejecting power-law hypotheses for synthetic data.
• A robust power-law exponent of approximately 1.1 was established for the radionuclide half-life density.
• A strong correlation between decay rate and released energy was identified as a key factor, particularly for alpha emission, explaining the power-law behavior.

Conclusions:

• The probability distribution of radionuclide half-lives follows a power law with a specific exponent.
• Existing statistical fitting methods may require re-evaluation for broad-range nuclear data.
• The relationship between decay energy and disintegration type, especially alpha emission, provides a novel physical mechanism for power-law generation in nuclear processes.