Effects of self-consistency violation in Hartree-Fock RPA calculations for nuclear giant resonances revisited

We provide accurate assessments of the consequences of violations of self-consistency in Hartree-Fock-(HF) based random-phase approximation (RPA) calculations of the centroid energy E_cen of isoscalar and isovector giant resonances of multipolarities L=0-3 in a wide range of nuclei. This is done by carrying out highly accurate HF-RPA calculations neglecting the particle-hole (p-h) spin-orbit or Coulomb interaction in the RPA and comparing with the fully self-consistent HF-RPA results. We find that the shifts in the value of E_cen because of self-consistency violation associated with the spin-orbit and Coulomb interactions are comparable or larger than the current experimental errors in E_cen.