Core-polarization effects and effective charges in O and Ni isotopes from chiral interactions

Background: Many nuclear structure calculations, even for full configuration interaction approaches, are performed with input Hamiltonians represented in a truncated model space. These often require consistent transformations of the operators to account for the missing physics beyond the active space, so that several recent efforts have been devoted to find compatible derivations of the effective operators. The effective charges employed in the shell-model calculations, and fitted to reproduce experimental data, can be seen as the phenomenological counterpart of such renormalization for electromagnetic operators. Purpose: A coherent mapping of ab initio approaches into shell-model valence spaces requires a consistent derivation of effective electromagnetic operators. Here, we make a first step to lay the bases for their microscopic derivation in the context of the self-consistent Green's function approach. Methods: We compute electric quadrupole (E2) effective charges from microscopic theory by coupling the single-nucleon propagators to core-polarization phonons, derived consistently from a realistic nuclear interaction. Nuclear correlations are included nonperturbatively according to the third-order algebraic diagrammatic construction and the Faddeev random-phase approximation. The polarization effects are included by evaluating the Feynman diagrams that couple the intermediate multinucleon configurations to the single-particle transitions induced by the electromagnetic operator. Results: The effective charges for E2 static moments and transitions are computed for selected isotopes in the oxygen (O14, O16, O22, and O24) and nickel (Ni48, Ni56, Ni68, and Ni78) chains. The values found are orbital dependent, especially for the neutron effective charges, which also show a characteristic decreasing trend along each isotopic chain. In general, the values are compatible with the phenomenological ones commonly used for shell-model studies in the 0p1s0d and 1p0f0g92 valence spaces. Conclusion: The phenomenological shell-model effective charges can be explained through ab initio approaches, where the sole experimental input comes from the fitting of the realistic nuclear interaction. Effective electromagnetic operators can be derived, which are tailored for different valence spaces and for specific numbers of active nucleons.