The hyperfine structure (HFS) of a bound electron is modified by the self-interaction of the electron with its own radiation field. This effect is known as the self-energy correction. In this work, we discuss the evaluation of higher order self-energy corrections to the HFS of bound P states. These are expressed in a semianalytic expansion involving powers of Zα and ln(Zα), where Z is the nuclear charge number and α is the fine-structure constant. We find that the correction of relative order α (Zα)2 involves only a single logarithm ln(Zα) for P1/2 states [but no term of order α (Zα)2ln2(Zα)], whereas for P3/2 states, even the single logarithm vanishes. By a Foldy-Wouthuysen transformation, we identify a nuclear-spin-dependent correction to the electron's transition current, which contributes to the HFS of P states. A comparison of the obtained analytic results to a numerical approach is made.



Keywords and Phrases

Bound Electrons; Fine Structure Constants; Foldy-Wouthuysen Transformations; Higher Order; Hydrogenlike Ion; Hyperfine Splittings; Hyperfine Structure; Nuclear Charge Numbers; Numerical Approaches; QED Correction; Radiation Field; Relative Order; Self-energy Corrections; Self-interactions; Algebra

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Document Type

Article - Journal

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Final Version

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© 2010 American Physical Society (APS), All rights reserved.

Publication Date

01 Jan 2010

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Physics Commons