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 $E_{\mathrm{cen}}$ 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 $E_{\mathrm{cen}}$ because of self-consistency violation associated with the spin-orbit and Coulomb interactions are comparable or larger than the current experimental errors in $E_{\mathrm{cen}}$.

Figure 1

HF-RPA results for isoscalar strength functions of ${}^{208}\mathrm{Pb}$ for $L=0-3$ multipolarities are displayed. SC (full line) corresponds to the fully self-consistent calculation where LS (dashed line) and CO (dotted line) represent the calculations without the p-h spin-orbit and Coulomb interactions in the RPA, respectively. A magnified giant resonance is shown in the inset (lowest panel) for $L=3$. The Skyrme interaction SGII [25] was used.

Figure 2

Same as Fig. 1 but for isovector strength functions.