Lamb shift of 3P and 4P states and the determination of alpha

The fine-structure interval of P states in hydrogenlike systems can be determined theoretically with high precision, because the energy levels of P states are only slightly influenced by the structure of the nucleus. Therefore a measurement of the fine structure may serve as an excellent test of QED in bound systems, or alternatively as a means of determining the fine-structure constant alpha with very high precision. In this paper an improved analytic calculation of higher-order binding corrections to the one-loop self-energy of 3P and 4P states in hydrogenlike systems with a low nuclear charge number Z is presented. The method of calculation has been described earlier by Jentschura and Pachucki [Phys. Rev. A 54, 1853 (1996)], and is applied hereto the excited P states. Because of the more complicated nature of the wave functions and the bound-state poles corresponding to decay of the excited states, the calculations are more complex. Comparison of the analytic results to the extrapolated numerical data for high-Z ions [Mohr and Kim, Phys. Rev. A 45, 2727 (1992)] serves as an independent test of the analytic evaluation. Theoretical values for the Lamb shift of the P states and for the fine-structure splittings are given.