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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.08575 |
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| _version_ | 1866912026449674240 |
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| author | Yang, San-Jiang Chi, Jing Zhou, Wan-Ping Tang, Li-Yan Zhong, Zhen-Xiang Shi, Ting-Yun Qiao, Hao-Xue |
| author_facet | Yang, San-Jiang Chi, Jing Zhou, Wan-Ping Tang, Li-Yan Zhong, Zhen-Xiang Shi, Ting-Yun Qiao, Hao-Xue |
| contents | In this article we propose a simple approach for the precision calculation of Bethe logarithm. The leading contributions are obtained using specific operators, while the remaining terms are eliminated by adjusting the parameter $λ$. Through the use of dimensional regularization, singular divergences are algebraically canceled. Compared to the standard form of Bethe logarithm, our approach significantly reduces the complexity of constructing pseudostates in numerical evaluations. Using this approach we obtain a very highly precise result of Bethe logarithm for the ground state of the hydrogen, achieving 49 significant digits. And for multi-electron systems this approach appears simplicity and efficiency as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Simple approach for precision calculation of Bethe logarithm Yang, San-Jiang Chi, Jing Zhou, Wan-Ping Tang, Li-Yan Zhong, Zhen-Xiang Shi, Ting-Yun Qiao, Hao-Xue Atomic Physics In this article we propose a simple approach for the precision calculation of Bethe logarithm. The leading contributions are obtained using specific operators, while the remaining terms are eliminated by adjusting the parameter $λ$. Through the use of dimensional regularization, singular divergences are algebraically canceled. Compared to the standard form of Bethe logarithm, our approach significantly reduces the complexity of constructing pseudostates in numerical evaluations. Using this approach we obtain a very highly precise result of Bethe logarithm for the ground state of the hydrogen, achieving 49 significant digits. And for multi-electron systems this approach appears simplicity and efficiency as well. |
| title | A Simple approach for precision calculation of Bethe logarithm |
| topic | Atomic Physics |
| url | https://arxiv.org/abs/2409.08575 |