-decay half-life is a key quantity for nuclear structure and nucleosynthesis studies. There exist large uncertainties in the contributions of allowed and forbidden transitions to the total -decay life, which limits the resolution of the predicted -decay half-life. We systematically study the contribution of the first forbidden (FF) transitions to the -decay half-life, and quantify it with a formula based on simple physics considerations. We also propose a new formula for calculation of the -decay half-life that includes the FF contribution. It is shown that the inclusion of the contribution of FF transitions significantly improves the precision of calculations of the -decay half-life. By fitting of the RQRPA results for neutron-rich , 57 isotopes and , 94 isotones, the formula for the contribution of the FF transitions gives similar results as the RQRPA calculations. However, because of limited experimental data for the branching ratios of unstable nuclei, the fit parameters are not fully constrained. Therefore, the proposed formula for the -decay half-life is more suitable for calculations of half-lives than of the FF contributions. The formula could be used to predict the -decay half-life in nuclear structure studies as well as nucleosynthesis calculations in stars.
A systematic analysis on experimental data of the half-lives of nuclear double- decays with two neutrinos ( ) is performed based on the analytical formula proposed by Primakoff and Rosen. We improve the formula by considering the shell effects and refining the energy dependence of the phase-space factor. This improved formula can closely describe all available experimental half-lives of decays, both for ground-state transitions and transitions from ground states of parent nuclei to the first excited states of daughter nuclei. The calculated half-lives agree with the experimental data of ground-state transitions of all known eleven nuclei with an average factor of 2.3. Further predictions are provided for -decay candidates with decay energies above 0.5 MeV. We compare different theoretical predictions and emphasize the importance of experimental measurements on the half-lives of double- transitions between the ground state of Ca, Ge, and Xe and the first excited states of their corresponding daughter nuclei, which will be very useful for understanding the underlying mechanisms of double- decays and for further studying the shell effects on nuclear transition matrix elements.
We have systematically analyzed the experimental -decay half-lives of waiting point heavy nuclei around neutron number N = 126. A new set of parameters for the exponential formula of -decay half-lives is proposed. The forbidden transition effects are included in the new set of parameters self-consistently. Theoretical -decay half-lives of nuclei around N = 126 are compared with recent theoretical results and experimental data. It is found that the new theoretical results are in better agreement with experimental data. The unknown -decay half-lives of some nuclei in this region are predicted for studies on nuclear structure far from stability and the nucleosynthesis in stars.
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