QED corrections of order alpha (Zalpha)^2 E_F to the hyperfine splitting of P_1/2 and P_3/2 states in hydrogenlike ions

Abstract

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 semi-analytic expansion involving powers of Zalpha and ln(Zalpha), where Z is the nuclear charge number and alpha is the fine-structure constant. We find that the correction of relative order alpha (Zalpha)^2 involves only a single logarithm ln(Zalpha) for P_1/2 states [but no term of order alpha (Zalpha)^2 ln^2(Zalpha), whereas for P_3/2 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.

12 oages; RevTeX

References in corpus (3)

• Complete two-loop correction to the bound-electron g factor
• Evaluation of the self-energy correction to the g-factor of S states in H-like ions
• Quantum electrodynamic corrections to the hyperfine structure of excited S states

Cited by in corpus (5)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Nuclear size correction to the Lamb shift of one-electron atoms
• Proposal for the determination of nuclear masses by high-precision spectroscopy of Rydberg states
• Self-Energy Correction to the Hyperfine Splitting for Excited States
• From First Principles of QED to an Application: Hyperfine Structure of P States of Muonic Hydrogen