s . at om - p h ] 2 3 M ay 1 99 7 Self - energy correction to the hyperfine structure splitting of the 1 s and 2 s states in hydrogenlike ions

The one-loop self-energy correction to the hyperfine structure splitting of the 1s and 2s states of hydrogenlike ions is calculated both for the point and finite nucleus. The results of the calculation are combined with other corrections to find the ground state hyperfine splitting in lithiumlike 209 Bi 80+ and 165 Ho 64+. The recent experimental investigation of the ground-state hyperfine splitting of 209 Bi 82+ [1] and 165 Ho 66+ [2] shows that the present experimental accuracy is much higher than the accuracy of the corresponding theoretical values. At present, measurements of the ground state hyperfine splitting of lithium-like ions are designed. In this connection a necessity of an accurate calculation of the QED corrections to the hyperfine splitting of the 1s and 2s states of highly charged ions is obvious. The one-loop self-energy correction to the first-order hyperfine interaction for the ground state of hydrogenlike ions in the case of an extended nucleus was calculated in [3] in a wide interval Z. In the case of Z = 83 and a point nucleus such a calculation was done in [4]. In the present work we recalculate the self-energy correction for the 1s state and present results for the 2s state. The calculation was made using the full-covariant scheme based on an expansion of the Dirac-Coulomb propagator in terms of interactions with the external potential [5, 6]. The self energy contribution to the hyperfine splitting is defined by the diagrams shown in Fig.1 where the dotted line denotes the hyperfine interaction. The formal expressions for these diagrams can easily be derived by the two-time Green function method [7]. The diagrams in Fig.1a are conveniently divided into irreducible and reducible parts. The reducible part is 1