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Nuclear mass, β-decay half-life, and neutron-capture rate are the most important nuclear physics inputs for rapid-neutron capture process (r-process) simulations. Nuclear mass can directly impact the abundance ratio of neighboring isotopes during the (n, γ)-(γ, n) equilibrium stage. On the other hand, nuclear mass influences the predictions of β-decay half-lives and the neutron-capture rates, thus indirectly impacting the r-process simulation. Currently, only about 3000 nuclear masses have been precisely measured in experiments, and many of the nuclear masses involved in r-process simulations can only be predicted by theory models. However, when extrapolating nuclear masses towards the neutron drip line, there are large discrepancies between the predictions of different mass models, which inevitably affects the predictions of β-decay half-lives and neutron-capture rates. In this work, ten mass models are employed to systematically study the impact of nuclear mass uncertainties on β-decay half-lives and neutron-capture rates. The β-decay half-lives and neutron-capture rates are calculated by the β-decay half-life semi-empirical formula and TALYS code, respectively. It has been found that the uncertainties in nuclear mass predictions among different mass models can reach 10 MeV in the neutron-rich region; the differences between the maximum and minimum masses predicted by these models even exceed 30 MeV for some nuclei. For the predictions of β-decay energy $Q_{\beta}$ and $(\rm n,\gamma)$ reaction energy $Q_{(\rm n,\gamma)}$, there are large deviations mainly around the neutron magic numbers and close to the neutron drip line, with uncertainties about 1 MeV and 2 MeV, respectively. The impact of mass uncertainties on the β-decay half-lives is about 0.6 orders of magnitude for neutron-rich nuclei. The uncertainties of neutron-capture rates increase significantly when extrapolating towards the neutron-rich region. At the temperature of $T=10^9$ K, the average uncertainties of neutron-capture rates range over 2~3 orders of magnitude for nuclei near neutron drip line. Taking $N=50,\;82,\;126,\;184$ isotones as examples, it is found that the differences between the maximum and minimum neutron-capture rates obtained from various nuclear mass models even exceed 10 orders of magnitude for some nuclei. The $Q_{(\rm n,\gamma)}$ directly impacts the trend of the neutron-capture rates, and the neutron-capture rates are very sensitive to the uncertainties of $Q_{(\rm n,\gamma)}$ for neutron-rich nuclei. In addition, the effect of temperature on neutron-capture rates has also been investigated, and it is found that the increase in temperature can reduce the impact of mass uncertainties on the predictions of neutron-capture rates for neutron-rich nuclei. In this work, the β-decay half-lives and neutron-capture rates are calculated based on ten mass tables. Therefore, more self-consistent nuclear physics inputs will be provided for the simulation of the r-process. The datasets presented in this paper are openly available at
https://www.doi.org/10.57760/sciencedb.j00213.00222 .-
Keywords:
- r-process /
- nuclear mass /
- β-decay half-life /
- neutron-capture rate
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图 1 各原子核质量模型与FRDM2012模型预言的Ni、Sn和Pb同位素质量之差. 黑色实心圆表示核质量实验值与FRDM2012预测值的差值
Figure 1. The differences between the mass predictions of various nuclear mass models and FRDM2012 model for Ni, Sn, and Pb isotopes, solid black circles denote the differences between experimental masses and the predictions of FRDM2012.
图 2 核质量 M、β衰变能$ Q_{\beta} $以及(n, γ)反应能$ Q_{(\rm n, \gamma)} $的不确定性. 灰色实线表示相应实验值范围的边界, 图中显示了参考文献[75]的r-过程路径以供参考, 由黑色实线表示, 该路径是基于经典r-过程模型预测的.
Figure 2. Uncertainties of nuclear mass M, β-decay energy $ Q_{\beta} $, and the reaction energy of (n, γ) $ Q_{(\rm n, \gamma)} $. The grey solid lines denote the boundaries of the corresponding experimental data ranges. The figure also shows the r-process path taken from Ref. [75] for guiding eyes, represented by the black solid lines, which is predicted based on the classical r-process model.
图 4 通过各种质量模型得到的理论β衰变半衰期对数的最大值和最小值的差异. 实验半衰期原子核的边界由灰色实线表示. 图中显示了参考文献[75]的r-过程路径以供参考, 由黑色实线表示
Figure 4. The differences between the maximum and minimum values of the logarithm of theoretical β-decay half-lives obtained by various nuclear mass models. The boundary lines of nuclei with known half-lives in NUBASE2020 are shown by the grey solid lines. The figure also shows the r-process path taken from Ref. [75] for guiding eyes, represented by the black solid lines
图 5 在温度$ T_9=1 $时, 各质量模型预测的$ N=50, \; 82, \; 126, \; 184 $同中子素链的中子俘获率, 阴影区域表示$ Q_{(\rm n, \gamma)} $实验未知区域
Figure 5. Predictions of radiative neutron-capture rate for $ N=50, \; 82, \; 126, $ and $ 184 $ isotones at $ T_9=1 $ with different mass models. The shaded region denotes the $ Q_{(\rm n, \gamma)} $ experimental unknown region.
图 6 各质量模型预测的$ N=126, \; 184 $同中子素链的$ (\rm n, \gamma) $反应能$ Q_{(\rm n, \gamma)} $
Figure 6. $ (\rm n, \gamma) $ reaction energies $ Q_{(\rm n, \gamma)} $ of $ N=126, \; 184 $ isotones predicted by various nuclear mass models.
图 7 对于各质量模型, 133Cd、133Sn、133Sb以及197Hf中子俘获率随温度的变化
Figure 7. Radiative neutron-capture rates of 133Cd, 133Sn, 133Sb, and 197Hf as a function of temperature for various nuclear mass models.
图 8 在温度$ T_9=1, 10 $时, $ \sigma_{\rm rms}(\log_{10}(N_A \langle\sigma v \rangle )) $随与稳定线距离的分布
Figure 8. Distribution of $ \sigma_{\rm rms}(\log_{10}(N_A \langle \sigma v \rangle )) $ with respect to the distance from the β-stability line at $ T_9=1 $ and $ 10 $.
表 1 衰变半衰期半经验公式参数
Table 1. Parameters of the semi-empirical formula of β-decay half-lives
$ a_{1} $ $ a_{2} $ $ a_{3} $ $ a_{4} $ $ a_{5} $ $ a_{6} $ $ a_{7} $ $ a_{8} $ 15.87058 6.34170 0.45683 3.54478 5.24596 3.88535 1.08275 0.71482 
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表 2 TALYS输入文件中关键字及其相应的值
Table 2. Keywords and their corresponding values in the TALYS input file
关键字 projectile element mass ejectiles astro expmass massdir 值 n Th 292 g y n bml
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