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: Ē[ρp] = (2α/15π2)(π2 − 3 + 6 ln 2)App k2 p with ρp = k3 p/3π 2 the proton density and App ≈ 2 fm an effective (in-medium) scattering length. Hints for such a value of App come from phenomenological Skyrme forces and from the neutron matter equation of state. PACS: 12.38.Bx, 21.10.Sf, 31.15.Ew. A classic problem in nuclear structure theory is to understand the binding energy differences between mirror nuclei (i.e. nuclei with the same mass number A = Z +N but with the proton number Z and the neutron number N interchanged). If the strong nuclear force is charge symmetric, then these binding energy differences can be directly related to the well-understood Coulomb interaction between the protons. However, as shown long ago by Nolen and Schiffer [1, 2] the experimental binding energy differences are systematically (by about 7%) larger than the ones calculated with a charge symmetric strong interaction and realistic nuclear wave functions (reproducing e.g. elastic electron-scattering data). This discrepancy which ranges from fairly light up to the heaviest available mirror nuclei is called the Nolen-Schiffer anomaly. It is generally agreed that both nuclear correlations [3] and a charge-symmetry breaking strong interaction are important for its understanding. Recently, Brown et al. [4] have performed a systematic study of these binding energy differences the mass region A ≤ 60 using the Skyrme-Hartree-Fock method. They have found that the anomaly can be resolved by either dropping the (weakly) attractive Coulomb exchange term in the nuclear energy density functional (see eqs.(5,7) below) or by introducing a chargesymmetry breaking delta-force which splits the proton-proton and neutron-neutron effective s-wave interactions. The strength of the adjusted charge-symmetry breaking interaction comes out, however, a factor 3 to 4 larger than expected from some high-precision nucleon-nucleon potentials (such as AV18 [5] or CDBonn [6]). Henley and Krein [7] suggested an alternative explanation of the Nolen-Schiffer anomaly based on the quark substructure of nucleons in the nuclear medium. In their Nambu-Jona-Lasinio model the down-up-quark mass difference induces, driven by the partial restoration of chiral symmetry, a substantial reduction of the neutron-proton mass difference in the nuclear medium (see Fig. 2b in ref.[7]). Clearly, any decrease of the neutron-proton mass difference will help to resolve the Nolen-Schiffer anomaly, since the calculated binding energy differences of mirror nuclei are based on the free neutronproton mass difference of 1.293 MeV. For a similar approach using the quark-meson coupling