A Simple approach for precision calculation of Bethe logarithm

San-Jiang Yang, Jing Chi, Wan-Ping Zhou, Li-Yan Tang, Zhen-Xiang Zhong, Ting-Yun Shi, Hao-Xue Qiao
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Abstract

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 $\lambda$. 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.
精确计算贝特对数的简单方法
在本文中,我们提出了一种精确计算对数的简单方法。我们使用特定的运算符来获得前导贡献,而其余项则通过调整参数$\lambda$来消除。通过使用维度正则化,奇异发散在代数上被消除。与贝特对数的标准形式相比,我们的方法大大降低了数值评估中构建伪态的复杂性。利用这种方法,我们获得了非常精确的氢基态贝特对数结果,达到了 49 位有效数字。对于多电子系统,这种方法也显得简单高效。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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