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

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

2004-06-07

arxiv.org/abs/nucl-th/0406013v1

Phys.Rev. C70 (2004) 014308

Physics

Nuclear Physics

Nuclear Theory

Revtex file (11 pages), Accepted for the publication in Phys. Rev. C

Scientific paper

10.1103/PhysRevC.70.014308

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 $^{90}$Zr and $^{208}$Pb nuclei for several Skyrme type effective nucleon-nucleon interactions having a wide range of nuclear matter incompressibility ($K_{nm} \sim 215 - 275$ MeV) and symmetry energy ($J \sim 27 - 37$ MeV) indicate that the net uncertainty ($\delta E_c \sim 0.3$ MeV) is comparable to the experimental one.

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