一种用于Bethe对数精密计算的简单方法
A Simple approach for precision calculation of Bethe logarithm
AI总结：
本研究提出一种Bethe对数精密计算的简单方法，通过特定算符取主导贡献、调$\lambda$消余项、维数正规化抵消发散，大幅降低数值计算中赝态构造复杂度，氢原子基态结果达49位有效数字，多电子体系同样简便高效。
摘要：
本文提出了一种用于Bethe对数精密计算的简单方法。我们利用特定算符得到主导贡献，同时通过调节参数$\lambda$消去剩余项。借助维数正规化方法，奇异发散项可通过代数方式抵消。与Bethe对数的标准形式相比，我们的方法显著降低了数值计算中构造赝态的复杂度。利用该方法，我们得到了氢原子基态Bethe对数的极高精度结果，达到49位有效数字。对于多电子体系，该方法同样表现出简便性与高效性。
英文摘要：
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.
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