Title: Application of the Most Frequent Value Method for $^{39}$Ar Half-Life Determination Show Chinese title

Title: 最频繁值法在$^{39}$阿尔法半衰期测定中的应用

Abstract: 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. Show Chinese abstract

Abstract: 采用一种基于稳健统计分析的评估方法来分析$^{39}$氩同位素半衰期的历史测量数据。该方法结合了最频值（MFV）法与自助法（bootstrap analysis），提供了一种更可靠的估算$^{39}$氩同位素半衰期的方式。结果显示，其半衰期为 T1/2(MFV) = 268.2 + (3.1) - (2.9) 年，不确定性对应于 68% 的置信水平。这一不确定性比 Stoenner 等人（1965年）重新计算的最精确测量值小三倍，也比核数据表中采用的半衰期值小 2.7 倍。最近，在不同地下设施中测定了大气氩中$^{39}$氩的 β 衰变具体活性。将 MFV 方法应用于这些测量数据，得到具体活性 SA($^{39}$氩/氩)(MFV) = 0.966 + (0.010) - (0.018) Bq/kg(大气氩)，其不确定性同样对应于 68% 的置信水平。本文还讨论了利用大气氩中$^{39}$氩的具体活性来确定$^{39}$氩同位素半衰期的方法。