Fully Self-Consistency in Relativistic Random Phase Approximation

Fully self-consistent relativistic random phase approximation (RRPA) is built on the relativistic mean field ground state with a non-linear relativistic Lagrangian. The consistency requires that the same effective interaction is adopted to simultaneously describe both the ground states and the excited states of the nucleus. Reliable and accurate numerical results of the nuclear giant resonances obtained in the RRPA require fully consistent calculations. In some excitation modes they are extremely sensitive to consistent treatment, e.g., such as isoscalar giant monopole and dipole resonances (ISGMR and ISGDR). In this work we perform the numerical calculations in the case of ISGDR for ²⁰⁸Pb and check the consistency. The spurious state in the ISGDR vanishes once the full self-consistency is achieved.