The efficient and simple B-splines variational method is successfully used to calculate Bethe logarithm for the hydrogen atom in the velocity and length gauges. The ground state Bethe logarithm of hydrogen with fourteen accurate figures is obtained in the velocity gauge, and in the length gauge the ground state value has eleven accurate figures. Present velocity- and length-gauge results for the n s, n p, n d, and n f states up to n = 200 of hydrogen are above the 10 −10 level of relative difference, which represent the successful variational attempt to calculate Bethe logarithm of hydrogen in the velocity and length gauges. In addition, the B-splines variational method is successfully extended to calculate Bethe logarithm for the helium atom combined with configuration interaction. Results of numerical calculations for n 1,3 S up to n = 8 states are presented in the acceleration gauge, the velocity gauge, and a hy...

中文翻译：

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使用不同规格的B样条计算氢和氦的Bethe对数

有效且简单的B样条变分方法已成功用于计算速度和长度规中氢原子的Bethe对数。在速度计中获得具有14个精确数字的氢的基态Bethe对数，在长度计中，基态值具有11个精确数字。当前ns，np，nd和nf态的速度和长度规结果，直到n = 200的氢都在相对差的10 -10水平以上，这表示成功进行了变分计算以计算Bethe的氢对数速度和长度规。此外，成功地扩展了B样条变分方法，以结合组态相互作用计算氦原子的Bethe对数。n 1的数值计算结果