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中高Z元素原子、离子的电子碰撞电离与激发截面快速计算方法

周旭 王川 胡荣豪 陶治豪 邓小良 梁亦寒 李晓亚 吕蒙 祝文军

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中高Z元素原子、离子的电子碰撞电离与激发截面快速计算方法

周旭, 王川, 胡荣豪, 陶治豪, 邓小良, 梁亦寒, 李晓亚, 吕蒙, 祝文军

A Fast Computation Approach of Electron-Impact Ionization and Excitation Cross-sections for Atoms and Ions of Middle and High-Z Elements

Zhou Xu, Wang Chuan, Hu Ronghao, Tao Zhihao, Deng Xiaoliang, Liang Yihan, Li Xiaoya, Lv Meng, Zhu Wenjun
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  • 中高Z元素的原子数据如碰撞电离和碰撞激发截面在聚变工程、X射线与物质相互作用等工程、研究领域有非常广泛的需求。高能量密度等离子体中存在从基态到激发态的原子和各价态离子,其碰撞电离和碰撞激发截面需要分别计算。本文以73号元素钽(Ta)为例,基于相对论性Dirac-Fock理论和扭曲波模型计算了基态Ta原子到Ta72+离子在入射电子能量范围为0-150 keV的碰撞电离与碰撞激发截面,并与相关实验和理论模型符合较好。通过分析Ta的碰撞电离和碰撞激发截面数据中的规律,给出两种减少计算量的方法:对初态能级进行随机抽样、筛去贡献小的反应道,并对计算量的优化程度和误差做出评估。最终结果可在误差5%内将计算效率提高一个量级。该方法可推广至其它中高Z元素的计算。
    The atomic data of middle and high-Z elements, such as electron-impact ionization and excitation cross-sections, find extensive applications in fields such as fusion science and X-ray interactions with matter. There are atoms and ions in high energy density plasma with different charge states and energy states from ground states to highly excited states, and the cross-sections of each charge state and energy state need to be calculated. The bottleneck limiting computational performance is the unavoidable relativistic effects of middle to high-Z atoms and the incredibly complex electronic configurations. Taking tantalum (Ta) as an example, by using the relativistic Dirac-Fock theory and distorted wave model, we computed the electron-impact ionization and excitation cross-sections of Ta from the ground state atom up to Ta72+ with the incident electron energy range of 0-150keV. The detailed configuration accounting (DCA) reaction channel cross-sections are derived by summing and weighting the original detailed level accounting (DLA) cross-sections. After examining the data, two regularities are found. In terms of DLA, the pre-averaging DCA cross-sections have varying initial DLA energy levels but are typically close to one another, but there isn't a straightforward function that can explain the discrepancies between them. In terms of DCA, inner subshells typically contribute very little to the total cross-section as their ionization and excitation cross-sections are orders of magnitude smaller than those of outer subshells. We provide two techniques to reduce the computational costs based on the regularities. To minimize the overall number of DLA reaction channels used in the computation, the initial DLA energy levels can be randomly sampled. Through a Monte Carlo numerical experiment, we determine the appropriate number of sampling points that can reduce the total number of DLA channels by an order of magnitude while maintaining a 5% error margin. In terms of impact ionization, since small cross-section DCA channels are insignificant, only a tiny portion of the DCA channels are required to preserve a 95% accuracy of the entire cross-section. It is possible to use the analytical Binary Encounter Bethe (BEB) formula to determine which DCA channels should be neglected before the computation to reduce computational costs. In terms of electron-impact excitation, just the cross-sections of the same excited subshells as the preserved ionized subshells, which are determined in the previous electron-impact ionization (EII) calculation, are needed. Lastly, we compared our EII results with theoretical and experimental results. In the low incident electron energy range of below 2 keV, our results agree with the theoretical result of the 6s EII cross-section of the Ta atom and the experimental result of the total EII cross-section of the Ta1+ ion. In the high energy range of below 150 keV, our results are also consistent with the theoretical results of the 1s EII cross-section of the Ta atom and the experimental result of the 1s EII cross-section of the Cu atom. Our results reasonably matched the previous experiment and theoretical results in both low and high energy ranges, inner and outer subshells, indicating the accuracy of our calculation. The proposed optimizing strategy can be applied to various middle to high-Z elements and is compatible to most computation codes.
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