非S能级的双环Bethe对数
Two-Loop Bethe Logarithms for non-S Levels
摘要：
计算了类氢系统中P和D激发态的双环Bethe谱，并对所有具有较高角动量的态给出了估计。这些结果完善了我们对氢的P和D能级的认识，其数量级为α ^8 m_e c ^2，其中m_e是电子质量，c是光速，其数量级为Z ^6，其中Z是核电荷数。我们的解析和数值计算结果表明，对于D态和所有具有较高角动量的态，完全不存在（α/π）^2（Z α）^6 ln[（Z α）^（-2）] m_e c^2级的对数项。对于较高的激发P和D态，在数值计算中必须减去来自较低能级的一些极点。令人惊讶的是，我们发现，对于大角动量的态，“平方衰变率型”修正在数值上占主导地位，其数量级为（alpha/pi）^2（Z alpha）^6 m_e c ^2，并提供了大角动量量子数的里德堡态的整个B_60系数的估计。我们的结果达到了量子电动力学理论的兰姆位移的预测极限。
英文摘要：
Two-loop Bethe logarithms are calculated for excited P and D states in hydrogenlike systems, and estimates are presented for all states with higher angular momenta. These results complete our knowledge of the P and D energy levels in hydrogen at the order of alpha^8 m_e c^2, where m_e is the electron mass and c is the speed of light, and scale as Z^6, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (alpha/pi)^2 (Z alpha)^6 ln[(Z alpha)^(-2)] m_e c^2 for D states and all states with higher angular momenta. For higher excited P and D states, a number of poles from lower-lying levels have to subtracted in the numerical evaluation. We find that, surprisingly, the corrections of the "squared decay-rate type" are the numerically dominant contributions in the order (alpha/pi)^2 (Z alpha)^6 m_e c^2 for states with large angular momenta, and provide an estimate of the entire B_60-coefficient for Rydberg states with high angular momentum quantum numbers. Our results reach the predictive limits of the quantum electrodynamic theory of the Lamb shift.
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