  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 16O 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.
