Particle-vibration coupling for giant resonances beyond the diagonal approximation

A self-consistent particle-vibration coupling (PVC) model without diagonal approximation is presented. The diagonal approximation, that neglects completely the interaction between the doorway states, has been removed by taking into account the interaction between the two particle-holes inside the doorway states. As applications, isoscalar giant monopole, dipole, and quadrupole resonances in O-16 are investigated based on the use of Skyrme functionals. The diagonal approximation is found to clearly impact the strength distribution of the giant quadrupole resonance, and the description of the experimental data is improved without this approximation. The impact of the diagonal approximation is analyzed in detail, especially its effect on the eigenenergies and the induced coupling between neutron and proton particle-hole configurations. The latter is a direct and physically sound effect of the improvement on our formalism. The importance of using self-consistently the full effective interaction in the PVC vertex, and the effect of its renormalization via the subtraction method, are also discussed. For completeness, we also analyze the dependence of our results on the Skyrme parametrization.