QED corrections of order alpha (Zalpha)² EF to the hyperfine splitting of P₁/2 and P₃/2 states in hydrogenlike ions

الأصل · EN

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 P₁/2 states [but no term of order alpha (Zalpha)² ln²(Zalpha), 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.