Higher-order binding corrections to the Lamb shift of 2Pstates

Abstract

We present an improved calculation of higher-order corrections to the one-loop self-energy of 2P states in hydrogenlike systems with small nuclear charge Z. The method is based on a division of the integration with respect to the photon energy into a high- and a low-energy part. The high-energy part is calculated by an expansion of the electron propagator in powers of the Coulomb field. The low-energy part is simplified by the application of a Foldy-Wouthuysen transformation. This transformation leads to a clear separation of the leading contribution from the relativistic corrections and removes higher-order terms. The method is applied to the 2${\mathit{P}}_{1/2}$ and 2${\mathit{P}}_{3/2}$ states in atomic hydrogen. The results lead to theoretical values for the Lamb shifts and the fine-structure splitting. © 1996 The American Physical Society.