Bethe-logarithm calculation using the B-spline method
Yongbo Tang, Zhenxiang Zhong, Chengbin Li, Haoxue Qiao, and Tingyun Shi
Accepted
A method based on B-spline basis set is developed that significantly simplifies the Bethe logarithm calculations for the atomic hydrogen. Without any auxiliary optimization and extrapolation, this method not only can calculate the Bethe logarithms of low-lying states to high precision using relatively small basis sets, but can also calculate high-lying Rydberg states efficiently. For the ground state, the Bethe logarithm is calculated to 24 significant figures using 450 B-spline functions. For high-lying Rydberg states, we can reproduce all the results of Jentschura and Mohr [Phys. Rev. A 72, 012110 (2005)].