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Main Authors: Yang, San-Jiang, Chi, Jing, Zhou, Wan-Ping, Tang, Li-Yan, Zhong, Zhen-Xiang, Shi, Ting-Yun, Qiao, Hao-Xue
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.08575
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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