Hyperfine structure and bound-electron g-factor

Magnetic interactions between bound electrons and external magnetic fields are described by the additional interaction Hamiltonian 

The operators of the magnetic moments of electron and of the nucleus read 

For a free electron, the Dirac theory yields a value gfree = 2. Corrections to the free-electron g-factor are essentially due to the interaction with the free radiation field. The determination of the g-factor of a bound electron interacting with an additional, homogeneous magnetic field Bext via measurements of the induced energy shift on atomic levels is one of the basic experiments for testing QED. The deviation (g — 2) can be measured rather precisely. 

The generic magnetic interaction gives rise to a level energy shift 

Assuming, for example, a point-like atomic nucleus and taking into account the pure Coulomb potential, where the wave functions are analytically known, yields for the Is state (Breit 1928) 

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