Iterated and irreducible pion-photon exchange in nuclei

We calculate the contribution to the nuclear energy density functional which arises from iterated pion-photon exchange between nucleons. In heavy nuclei, this novel charge symmetry breaking interaction leads to an additional binding of each proton by about 0.2 MeV. Compared to that the analogous effect from irreducible pion-photon exchange is negligibly small. As a possible mechanism to resolve the Nolen-Schiffer anomaly we propose the iteration of one-photon exchange with an attractive short-range NN-interaction. The corresponding energy per proton reads: $\bar E[\rho_p]=(2\alpha/15\pi^2)(\pi^2 -3+6 \ln2) {\cal A}_{pp} k_p^2$ with $\rho_p =k_p^3/ 3\pi^2$ the proton density and ${\cal A}_{pp}\approx 2$fm an effective (in-medium) scattering length. Hints for such a value of ${\cal A}_{pp}$ come from phenomenological Skyrme forces and from the neutron matter equation of state.