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.
U. D. Jentschura and V. A. Yerokhin, "QED Corrections of Order α(Zα)²EF to the Hyperfine Splitting of P1/2 and P3/2 States in Hydrogenlike Ions," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 81, no. 1, pp. 012503-1-012503-10, American Physical Society (APS), Jan 2010.
The definitive version is available at https://doi.org/10.1103/PhysRevA.81.012503
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
International Standard Serial Number (ISSN)
Article - Journal
© 2010 American Physical Society (APS), All rights reserved.
01 Jan 2010