Title: On fluctuation properties of MACS Show Chinese title

Title: 关于MACS的涨落性质

Abstract: The Maxwellian Average Cross Section (MACS) is usually calculated with help of the statistical codes that do not take into account fluctuations of individual resonance parameters. The actual MACS can substantially deviate from its expectation value. This work focuses on description of various sources and aspects of these fluctuations. Simulated resonance sequences considering all the fluctuations involved in the statistical model are used for this purpose. Contribution of various sources of the fluctuations and neutrons with different orbital momenta are thoroughly investigated and described. Impact of available cross section data at low neutron energies is also checked. Based on this analysis simple empirical formulae for estimating relative fluctuations of MACS using solely $s$-wave resonance spacing $D_0$ and the temperature of the stellar environment are derived. It is shown that real nuclei follow the proposed formula well. The expected MACS fluctuations increase with $D_0$ and can be significant. While for isotopes with $D_0$ in eV range the possible deviation from calculated values are small, for nuclei with $D_0$ in the keV range the full-width half-maximum of the expected distribution is larger than about 25\% and 10\% for astrophysically relevant temperatures of $kT=8$ and 30 keV. At least for these nuclei the predictions from statistical codes must be taken with caution. Show Chinese abstract

Abstract: 麦克斯韦平均截面（MACS）通常借助不考虑单个共振参数波动的统计代码进行计算。 实际的MACS可能与其期望值有显著偏差。 本工作专注于描述这些波动的各种来源和方面。 为此，使用了考虑统计模型中所有波动的模拟共振序列。 各种波动来源以及不同轨道角动量中子的贡献得到了彻底的研究和描述。 也检查了低能中子截面数据的影响。 基于此分析，推导出了仅使用$s$波共振间距$D_0$和恒星环境温度的估计MACS相对波动的简单经验公式。 结果表明，实际核很好地遵循所提出的公式。 预期的MACS波动随着$D_0$的增加而增加，可能是显著的。 对于具有在电子伏特范围内的$D_0$的同位素，与计算值的可能偏差较小，而对于具有在千电子伏特范围内的$D_0$的核，在天体物理相关的温度为$kT=8$和30千电子伏特的情况下，预期分布的半高全宽大于约25%和10%。 至少对于这些核，统计代码的预测必须谨慎对待。