Evaluation of the self-energy correction to the $g$ factor of $S$ states in H-like ions

A detailed description of the numerical procedure is presented for the evaluation of the one-loop self-energy correction to the $g$ factor of an electron in the $1s$ and $2s$ states in H-like ions to all orders in $Z\alpha$.

Figure 1

Feynman diagrams representing the self-energy correction to the bound-electron $g$ factor. The double line indicates the bound-electron propagator and the wavy line that ends with a cross denotes the interaction with the external magnetic field.

Figure 2

The potential expansion of the vertex diagram. The single line indicates the free-electron propagator and the dashed line denotes the interaction with the Coulomb field of the nucleus. The terms of the potential expansion are referred to as the zero-potential, one-potential, and many-potential contributions.

Figure 3

The higher-order self-energy contribution $F_{\text{ho}}\left(Z\alpha \right)$ for the $1s$ and $2s$ electron $g$ factors in H-like ions.