Consequences of self-consistency violations in Hartree-Fock random-phase approximation calculations of the nuclear breathing mode energy

We provide for the first time accurate assessments of the consequences of violations of self-consistency in the Hartree-Fock based random phase approximation (RPA) as commonly used to calculate the energy E_c of the nuclear breathing mode. Using several Skyrme interactions we find that the self-consistency violated by ignoring the spin-orbit interaction in the RPA calculation causes a spurious enhancement of the breathing mode energy for spin unsaturated systems. Contrarily, neglecting the Coulomb interaction in the RPA or performing the RPA calculations in the TJ scheme underestimates the breathing mode energy. Surprisingly, our results for the ⁹⁰Zr and ²⁰⁸Pb nuclei for several Skyrme type effective nucleon-nucleon interactions having a wide range of nuclear matter incompressibility (K_nm∼215–275 MeV) and symmetry energy (J∼27–37 MeV) indicate that the net uncertainty (δE_c∼0.3 MeV) is comparable to the experimental one.