α decay half-life estimation and uncertainty analysis

Background: alpha decay is one of the most important decay modes of atomic nuclei. The half-life of alpha decay provides valuable information for nuclear structure study. Many theoretical models and empirical formulas have been suggested to describe the half-life of alpha decay as a function of decay energy (Q(alpha)), atomic number (Z), nucleon number (A), and other related variables. However, the analysis of theoretical uncertainty is rarely done for those alpha decay models. Purpose: We aim to perform a systematic and detailed study on the theoretical uncertainty of existing alpha decay formulas based on statistical methods. Methods: The nonparametric bootstrap method is used to evaluate the uncertainties of two alpha 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 alpha decay half-life. Results: If N > 126 and N <= 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 a shell correction term, a much larger systematic uncertainty is found if parameters obtained for N <= 126 nuclei are used to describe the half-lives of N > 126 nuclei. Based on the Bohr-Sommerfeld quantization condition and simple assumptions, a detailed shell correction term is obtained for N > 126 nuclei, for which the value is similar to that in NGNL. A global hindrance on the alpha decay process is found in oA_nc (oA_c) nuclei compared 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 parameter of angular momentum term in NGNL is obtained with large uncertainty and very sensitive to the selections of the dataset. The recently observed superallowed decay from Te-104 to Sn-100 is also discussed based on uncertainty analysis. Conclusions: The theoretical uncertainty of existing alpha decay formulas is successfully evaluated by the nonparametric bootstrap method, which simultaneously indicates the important effect in alpha decay, such as the shell effect and the pairing effect. In addition, statistical results show strong correlations between the parameters of the second and third terms in both UDL and NGNL, which demands further investigations.