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 2P1/2 and 2P3/2 states in atomic hydrogen. The results lead to theoretical values for the Lamb shifts and the fine-structure splitting.
U. D. Jentschura and K. Pachucki, "Higher-Order Binding Corrections to the Lamb Shift of 2P States," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 54, no. 3, pp. 1853-1861, American Physical Society (APS), Sep 1996.
The definitive version is available at https://doi.org/10.1103/PhysRevA.54.1853
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