The g factor of an electron or muon bound by an arbitrary central potential

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We consider the g factor of a spin-1/2 particle (electron or muon) bound by an arbitrary central field. We present an approach which allows one to express the relativistic g factor in terms of the binding energy. We derive the general expression for the correction to the g factor caused by a deviation of the central potential from the Coulomb one. As the application of this method, we consider the corrections to the g factor due to the finite nuclear size, including vacuum polarization radiative correction. The effect of the anomalous magnetic moment is also taken into account.