The Relativistic Random Phase Approximation (RRPA) is derived from the Time-dependent Relativistic Mean Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the ususal particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector meson fields which couple the αh-configurations with the phconfigurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the non-relativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained.

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A relativistic mean field description of collective excitations of atomic nuclei is studied in the framework of a fully self-consistent relativistic random phase approximation (RRPA). In particular, results of RRPA calculations of multipole giant resonances and of low-lying collective states in spherical nuclei are analyzed. 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. Two points are essential for the successful application of the RRPA in the description of dynamical properties of finite nuclei: (i) the use of effective Lagrangians with non-linear terms in the meson sector, and (ii) the fully consistent treatment of the Dirac sea of negative energy states.

We have examined within a fully self-consistent theoretical framework the energy difference between the anti-analog giant dipole resonance (AGDR) and the isobaric analog state (IAS), E AGDR − E IAS , as an indicator of the neutron skin and of the density behavior of the symmetry energy. We have improved two specific points in our HF+RPA calculations: (1) the exchange term of the two-body Coulomb interaction is treated exactly without Slater approximation; and (2) the two-parameters spin-orbit interaction is treated in a consistent way within the energy density functional theory. The estimated values for the neutron skin in 208 Pb and the slope parameter of symmetry energy are compared with previous analysis available in the literature.

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The isoscalar giant monopole resonances (ISGMRs) of hypernuclei , , and are investigated using a fully self-consistent Skyrme–Hartree–Fock plus random phase approximation method. The Skyrme-type forces, SGII, No.5 and SΛΛ1, are adopted to describe the nucleon–nucleon, Λ hyperon–nucleon and Λ hyperon–Λ hyperon (ΛΛ) interactions, respectively. For a given hyperon fraction, we find that effects of ΛΛ interaction on the properties of infinite symmetric nuclear matter and finite hypernuclei are very small. The ISGMR strengths are shifted to the high energy region when two Λ are added into normal nuclei. The changes are from two parts, one is due to the mean field calculations, and the other is from the residual interaction associated with Λ hyperons. The constrained energies are increased by about 0.5–0.7 MeV, which consequently enhances the effective incompressibility modulus of hypernuclei.