Application of the Most Frequent Value Method for $^{39}$Ar Half-Life Determination

An evaluation method supported by robust statistical analysis was used to analyze historical measurements of $^{39}$Ar half-life. The method, which combines the most frequent value (MFV) approach with bootstrap analysis, provides a more reliable way to estimate the half-life of $^{39}$Ar. The results show that the half-life is T1/2(MFV) = 268.2 + (3.1) - (2.9) years, with an uncertainty corresponding to the 68% confidence level. This uncertainty is three times smaller than the most precise re-calculated measurements by Stoenner et al. (1965) and 2.7 times smaller than the adopted half-life value in nuclear data sheets. Recently, the specific activity of the beta decay of $^{39}$Ar in atmospheric argon was measured in various underground facilities. Applying the MFV method to these measurements gives a specific activity of SA($^{39}$Ar/Ar)(MFV) = 0.966 + (0.010) - (0.018) Bq/kg(atmAr), with an uncertainty corresponding to the 68% confidence level. This paper also discusses the method used to determine the half-life of $^{39}$Ar using the specific activity of $^{39}$Ar in atmospheric argon.