### Abstract

The fine-structure interval of [Formula Presented] states in hydrogenlike systems can be determined theoretically with high precision, because the energy levels of [Formula Presented] 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 [Formula Presented] with very high precision. In this paper an improved analytic calculation of higher-order binding corrections to the one-loop self-energy of 3[Formula Presented] and 4[Formula Presented] states in hydrogenlike systems with a low nuclear charge number [Formula Presented] is presented. The method of calculation has been described earlier by Jentschura and Pachucki [Phys. Rev. A 54, 1853 (1996)], and is applied here to the excited [Formula Presented] 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-[Formula Presented] 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 [Formula Presented] states and for the fine-structure splittings are given.

Original language | English |
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Pages (from-to) | 1739-1755 |

Number of pages | 17 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 56 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1997 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics