Title: Statistical properties of neutron-induced reaction cross sections using random-matrix approach Show Chinese title

Title: 中子诱发反应截面的统计特性研究基于随机矩阵方法

Abstract: We investigate the statistical properties of neutron-induced nuclear reactions on $^{238}$U using the GOE-$S$-matrix model, in which the Gaussian Orthogonal Ensemble (GOE) is embedded into the scattering ($S$) matrix. The GOE-$S$-matrix model does not require any experimental values of the average level spacing $D$ and average decay width $\Gamma$ with their statistical distributions, but the model is fully characterized by the channel transmission coefficients used in the Hauser-Feshbach theory. We demonstrate that the obtained compound nucleus decay width distribution resembles the $\chi$-squared distribution with the degree of freedom greater than unity. This approach enables us to generate fluctuating cross sections while preserving requisite unitarity and accounting for interference between resonances. By comparing the calculated cross section distribution with that from $R$-matrix theory, we demonstrate a smooth transition from the resolved resonance region to the continuum region. Show Chinese abstract

Abstract: 我们使用GOE-$S$-矩阵模型研究中子诱发核反应在$^{238}$U上的统计特性，其中高斯正交系综（GOE）嵌入到散射（$S$）矩阵中。 GOE-$S$-矩阵模型不需要平均能级间距$D$和平均衰变宽度$\Gamma$的任何实验值及其统计分布，但该模型完全由哈瑟-费什巴赫理论中使用的通道传输系数表征。 我们证明获得的复合核衰变宽度分布类似于自由度大于一的$\chi$-平方分布。 这种方法使我们能够在保持必要单位性和考虑共振之间干涉的同时生成波动截面。 通过将计算得到的截面分布与$R$矩阵理论的结果进行比较，我们展示了从分辨共振区到连续区的平滑过渡。