Speaker
摘要
贝特-布洛赫(Bethe-Bloch)公式中平均激发能(I值)的准确确定一直是辐射屏蔽优化的难点，迫使工程设计往往依赖耗时的黑箱搜索算法或忽略化学键效应的布拉格加和定则(BAR)。本文提出了一种受局域等离子体近似(LPA)理论启发的半经验模型，揭示了宏观电子密度(ρe)与质子最大能量沉积(Eth)之间存在的稳定规律。通过对112种单质及复合材料的Geant4模拟分析，证明了ρe作为一个集体参量，能有效捕捉独立原子模型所忽略的凝聚态效应。研究发现，材料的I值与ρe遵循1/ρe∝I-2/3的标度关系，该指数偏离了理想电子气的理论预测值1/ρe∝I-2，反映了凝聚态物质中的几何约束与费米面效应。针对壳层结构引起的电子云体积异常，本文进一步提出了一种针对离子化合物的等电子修正方法，显著降低了预测误差。基于此，建立了利用单一变量ρe直接计算Eth的经验模型（R2>0.99989），并实现了屏蔽设计的逆向求解。与多目标遗传算法(NSGA-II)相比，该逆向设计在保证平均误差小于3.7%的同时，计算效率实现了5个数量级以上的提升。此外，本文还基于特征材料的反演策略给出了包含厚度变量的完整Eth(d,ρe)解析公式，为受质量与体积双重约束的空间辐射屏蔽设计提供了一种兼具物理解释性与计算高效性的解析方法。
Abstract
In the optimal design of radiation shielding, the shielding performance of known materials can be accurately calculated using the Bethe–Bloch formula. Nevertheless, practical design still relies on time‑consuming black‑box search algorithms. The optimal shielding materials obtained in this way not only lack physical justification but are also unconvincing: the algorithmic results are sometimes irreproducible, and outputs from different algorithms can differ substantially. This creates an urgent demand to clearly identify, through rigorous physical formulas, what the optimal shielding material is under given conditions and how to determine it uniquely. In this paper, we propose a semi-empirical model inspired by the Local Plasma Approximation (LPA) theory, revealing a robust scaling correlation between macroscopic electron density (ρe) and full absorption threshold (Eth). Through Geant4 simulation analysis of 112 elemental and composite materials, we demonstrate that ρe, as a collective parameter, effectively captures the condensed matter effects ignored by independent atom models. We observe a strong empirical correlation where the material's I-value and ρe follow a scaling relation of 1/ρe∝I-2/3. This exponent deviates from the theoretical prediction for an ideal electron gas (1/ρe∝I-2). To address volume anomalies caused by shell structures, we further propose an isoelectronic correction method for ionic compounds, which significantly reduces prediction errors. Based on this, we established an empirical model using the single variable ρe to directly calculate Eth (R2>0.99989) and implemented an inverse design solution for shielding. Compared to the Multi-objective Genetic Algorithm (NSGA-II), this inverse design method achieves a calculation efficiency improvement of over five orders of magnitude while maintaining the mean absolute percentage error (MAPE) of less than 4.6%. Furthermore, based on an inversion strategy using characteristic materials, we provide a complete analytical formula for Eth(d, ρe) including thickness variables. This offers an analytical method combining physical interpretability and computational efficiency for space radiation shielding design subject to dual mass and volume constraints.
| 关键词 | 平均激发能；阻止本领；壳层效应；电子密度；贝特-布洛赫公式 |
|---|---|
| Keywords | Mean Excitation Energy;Stopping Power;Shell Effect;Electron Density;Bethe-Bloch Formula |
