论文标题
$α$衰减半衰期估计和不确定性分析
$α$ Decay Half-life Estimation and Uncertainty Analysis
论文作者
论文摘要
非参数bootstrap方法用于评估两个$α$衰变公式，通用衰减法（UDL）和新的Geiger-Nuttall Law（NGNL）的不确定性。这样的方法可以同时获得每个参数的不确定性，每对参数之间的相关性以及每个公式的总，统计和系统的不确定性。分析中都使用了均匀的（EE）核和奇数-A（OA）核。收集的数据分为三个部分：EE核，无自旋或奇偶校验变化的OA核（OA \ _NC），以及具有自旋和/或奇偶校验变化的OA核（OA \ _C）。基于观察到的数据和相应计算之间的残基，统计和系统的不确定性是从总不确定性中分解出来的，从中，人们可以从中阐明壳结构，配对和角动量的影响，以及描述$α$ decay decay的半衰期。如果$ n> 126 $和$ n \ leqslant 126 $ nuclei被同时考虑，则观察到的半衰期和预测的半衰期之间残基的系统不确定性要大于分别考虑这些组。没有壳校正项，如果使用$ n \ leqslant 126 $ nuclei获得的参数来描述$ n> 126 $ nuclei的半衰期，则发现更大的系统不确定性。与EE（OA \ _NC）核进行比较的OA \ _NC（OA \ _C）核中发现了$α$衰减过程的全局障碍。如果使用了从EE（OA \ _NC）核获得的参数，则通常会被大型系统的不确定性低估OA \ _nc（OA \ _C）核的半衰期，这可能与配对效应和角动量的贡献有关。最近，最近观察到的超毛衰变从$^{104} $ te到$^{100} $ sn也是根据不确定性分析讨论的。 （由于长度限制，摘要未完全呈现）
The non-parametric bootstrap method is used to evaluate the uncertainties of two $α$ decay formulas, the universal decay law (UDL) and the new Geiger-Nuttall law (NGNL). Such a method can simultaneously obtain the uncertainty of each parameter, the correlation between each pair of parameters, and the total, statistical, and systematic uncertainties of each formula. Both even-even (ee) nuclei and odd-A (oA) nuclei are used in the analysis. The collected data are separated into three parts: ee nuclei, oA nuclei without spin or parity change (oA\_nc), and oA nuclei with spin and/or parity change (oA\_c). Based on the residues between observed data and corresponding calculations, the statistical and systematic uncertainties are decomposed from the total uncertainty, from which one can clarify the effects from the shell structure, pairing, and angular momentum change on describing $α$ decay half-life. If $N > 126$ and $N \leqslant 126$ nuclei are considered together, the systematic uncertainty of residues between observed and predicted half-lives are larger than if those groups are considered separately. Without shell correction term, a much larger systematic uncertainty is found if parameters obtained for $N \leqslant 126$ nuclei are used to describe the half-lives of $N > 126$ nuclei. A global hindrance on the $α$ decay process is found in oA\_nc (oA\_c) nuclei comparing with ee (oA\_nc) nuclei. If parameters obtained from ee (oA\_nc) nuclei are used, the half-lives of oA\_nc (oA\_c) nuclei are generally underestimated with large systematic uncertainties, which can be related to the contribution of pairing effect and angular momentum. The recently observed superallowed decay from $^{104}$Te to $^{100}$Sn is also discussed based on uncertainty analysis. (Abstract is not fully presented because of length limitation)
