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The dipole excitations for calcium and zirconium isotopes are studied withinthe fully self-consistent Hartree-Fock mean field incorporated with therenormalized random-phase approximation (RRPA) using the Skyrme interactionSLy5. The RRPA takes into account the effect of ground-state correlationsbeyond RPA owing to the Pauli principle between the particle-hole pairs thatform the RPA excitations as well as the correlations due to theparticle-particle and hole-hole transitions, whose effects are treated here inan effective way. By comparing the RPA results with the RRPA ones, which areobtained for isoscalar (IS) and isovector (IV) dipole excitations in $^{48, 52,58}$Ca and $^{90, 96, 110}$Zr, it is shown that ground-state correlationsbeyond the RPA reduce the IS transition strengths. They also shift up theenergy of the lowest IV dipole state and slightly push down the peak energy ofthe IV giant dipole resonance. As the result, the energy-weighted sums ofstrengths of both IS and IV modes decrease, causing the violation of thecorresponding energy-weight sum rules (EWSR). It is shown that this sum ruleviolation can be eliminated by taking into account the contribution of theparticle-particle and hole-hole excitations together with the particle-holeones in a simple and perturbative way. Consequently, the ratio of theenergy-weighted sum of strengths of the pygmy dipole resonance to that of thegiant dipole resonance increases.

Effective restoration of dipole sum rules within the renormalized random-phase approximation