QED corrections of order α(Zα)2EF to the hyperfine splitting of P1/2 and P3/2 states in hydrogenlike ions - Jentschura, Ulrich D.; Yerokhin, Vladimir (Physical review. A, Atomic, molecular, and optical physics, 2010)
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.