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Two-Loop Bethe Logarithms For Non- S Levels, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

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 α⁸ m_ec², where me is the electron mass and c is the speed of light, and scale as Z⁶, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (απ)² (Zα)⁶ ln [(Zα)^-2] …