A consistent approach in the relativistic random phase approximation for stable and exotic nuclei

Abstract

A fully consistent Relativistic Random Phase Approximation (RRPA) is studied in the sense that the relativistic mean filed (RMF) wave function of the nucleon and the RRPA renormalization are calculated in a same effective Lagrangian. In the no-sea approximation of RMF theory, the RRPA configuration space includes not only the usual particle-hole states, but also the pairs formed from the occupied Fermi states and Dirac states. The importance of the inclusion of this type of pairs formed between Dirac and Fermi states is investigated and large effects are observed for isoscalar modes, especially the monopole modes. It is found that the main contribution from the pairs of Fermi and Dirac states have their origin in the exchange of scalar mesons, while the effects of the vector mesons are largely suppressed. The RRPA is formally derived from Time-dependent RMF theory (TDRMF) in the limit of small amplitude oscillations. Numerical results of relativistic RPA are checked with the constrained relativistic mean field model and the TDRMF for the monopole mode. By using effective Lagrangians, which in the mean-field approximation provide an accurate description of ground-state properties, an excellent agreement with experimental data is also found for the excitation energies of low-lying collective states and of giant resonances. Applications to exotic nuclei, such as Ca-isotopes are also presented.