Nuclear reaction rate ($\lambda$) is a significant factor in the process of nucleosynthesis. A multi-layer directed-weighted nuclear reaction network in which the reaction rate as the weight, and neutron, proton, $^4$He and the remainder nuclei as the criterion for different reaction-layers is for the first time built based on all thermonuclear reactions in the JINA REACLIB database. Our results show that with the increase of the stellar temperature ($T_{9}$), the distribution of nuclear reaction rates on the $R$-layer network demonstrates a transition from unimodal to bimodal distributions. Nuclei on the $R$-layer in the region of $\lambda = [1,2.5\times10^{1}]$ have a more complicated out-going degree distribution than the one in the region of $\lambda = [10^{11},10^{13}]$, and the number of involved nuclei at $T_{9} = 1$ is very different from the one at $T_{9} = 3$. The redundant nuclei in the region of $\lambda = [1, 2.5\times10^{1}]$ at $T_{9} = 3$ prefer $(\gamma,p)$ and $({\gamma,\alpha})$ reactions to the ones at $T_{9}=1$, which produce nuclei around the $\beta$ stable line. This work offers a novel way to the big-data analysis on nuclear reaction network at stellar temperatures.

中文翻译：

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反应速率加权多层核反应网络

核反应速率（$\lambda$）是核合成过程中的一个重要因素。首次建立了以反应速率为权重，以中子、质子、$^4$He和剩余核为不同反应层判据的多层定向加权核反应网络。 JINA REACLIB 数据库中的热核反应。我们的结果表明，随着恒星温度（$T_{9}$）的增加，$R$ 层网络上的核反应速率分布表明从单峰分布到双峰分布的转变。$\lambda = [1,2.5\times10^{1}]$区域内$R$层上的核具有比$\lambda = [10 ^{11},10^{13}]$, 并且在 $T_{9} = 1$ 处涉及的核数与在 $T_{9} = 3$ 处的核数有很大不同。$\lambda = [1, 2.5\times10^{1}]$ 区域中的冗余核在 $T_{9} = 3$ 更喜欢 $(\gamma,p)$ 和 $({\gamma,\alpha })$ 对 $T_{9}=1$ 的反应，在 $\beta$ 稳定线周围产生原子核。这项工作为恒星温度下核反应网络的大数据分析提供了一种新方法。