Abstract
In the framework of the quasipotential method the covariant expression for the two-particle vertex operator is obtained. The nuclear structure corrections of orders (Zα)^4, (Zα)^5 including recoil effects to gyromagnetic factors of the bound electron and muon are calculated. Numerical value of the contribution of order (Zα)^5 is obtained by means of the dipole parameterization for the nuclear charge form factor in the range of the nuclear charges Z=7-32.
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