Wichmann-Kroll potentials, can be found, e.g., in Ref. [56]. The contributions of these diagrams are given by Δ E VP( A ) SQED = Δ E VP( A 1) SQED + Δ E VP( A 2) SQED , (51) Δ E VP( A 1) SQED = 2 ∑ n 1 , 2 $^{′}$〈 Pa | U el VP | n$_{1}$ 〉 〈 n$_{1}$ | T$_{0}$ | n$_{2}$ 〉〈 n$_{2}$Pb | I (Δ) | QaQb 〉 ( ε$_{Pa}$ − ε$_{n}$$_{1}$ )( ε$_{Pa}$ − ε$_{n}$$_{2}$ ) , (52) Δ E VP( A 2) SQED = 2 ∑ n 1 , 2 $^{′}$〈 Pa | U el VP | n$_{1}$ 〉 〈 n$_{1}$Pb | I (Δ) | n$_{2}$Qb 〉〈 n$_{2}$ | T$_{0}$ | Qa 〉 ( ε$_{Pa}$ − ε$_{n}$$_{1}$ )( ε$_{Qa}$ − ε$_{n}$$_{2}$ ) , (53) Δ E VP( B ) SQED = 2 ∑ n 1 , 2 ′ 〈 Pa | T$_{0}$ | n$_{1}$ 〉 ε$_{Pa}$ − ε$_{n}$$_{1}$ 〈 n$_{2}$ | U el VP | n$_{1}$ 〉 〈 n$_{2}$Pb | I (Δ) | QaQb 〉 ε$_{Pa}$ − ε$_{n}$$_{2}$ , (54) Δ E VP( E ) SQED = Δ E VP( E 1) SQED + Δ E VP( E 2) SQED , (55) Δ E VP( E 1) SQED = 2 ∑ n 1 , 2 $^{′}$〈 Pa | U el VP | n$_{1}$ 〉 〈 Pb | T$_{0}$ | n$_{2}$ 〉〈 n$_{1}$n$_{2}$ | I (Δ) | QaQb 〉 ( ε$_{Pa}$ − ε$_{n}$$_{1}$ )( ε$_{Pb}$ − ε$_{n}$$_{2}$ ) , (56) Δ E VP( E 2) SQED = 2 ∑ n 1 , 2 $^{′}$〈 Pa | U el VP | n$_{1}$ 〉 〈 n$_{1}$Pb | I (Δ) | Qan$_{2}$ 〉〈 n$_{2}$ | T$_{0}$ | Qb 〉 ( ε$_{Pa}$ − ε$_{n}$$_{1}$ )( ε$_{Qb}$ − ε$_{n}$$_{2}$ ) . (57) The diagrams of type C (so-called ’magnetic-loop’ diagrams) involve the matrix elements of the magnetic-field-induced vacuum-polarization potential U ml $_{VP}$. It also requires the charge renormal- ization to make it finite. Our present treatment of this poten tial is restricted to the Uehling (free- electron-loop) approximation. The expression for this potential in the Uehling approximation in case of the hyperfine interaction can be found in Ref. [57] forthe point-dipole nuclear model, and in Ref. [47] for the sphere model of the nuclear magnetization distribution. In case of the g factor this potential in the Uehling approximation is equal to zero. The contribution of the diagrams of type C is given by Δ E VP( C ) SQED = 2 ∑ n 1 $^{′}$〈 Pa | U ml VP | n$_{1}$ 〉 〈 n$_{1}$Pb | I (Δ) | QaQb 〉 ε$_{Pa}$ − ε$_{n}$$_{1}$ . (58) The diagram of type F contains the interelectronic-interaction operator modifi ed by the vacuum polarization I$_{VP}$ ( ω ) . Our present treatment of this term is restricted to the Uehling approximation. 14