The time-dependent relativistic mean-field theory and the random phase approximation

The Relativistic Random Phase Approximation (RRPA) is derived from the Time -Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small am plitude oscillations. In the nosea approximation of the RMF theory, the RRP A configuration space includes not only the usual particle-hole ph-states, but also alphah-configurations, i.e. pairs formed from occupied states in t he Fermi sea and empty negative-energy states in the Dirac sea. The contrib ution of the negative-energy states to the RRPA matrices is examined in a s chematic model, and the large effect of Dirac-sea states on isoscalar stren gth distributions is illustrated for the giant monopole resonance in Sn-116 . It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the alphah-configurations with the ph-configurations are strongly reduced with respect to the corresponding ma trix 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 pr onounced effect on giant resonances with excitation energies in the MeV reg ion. The influence of nuclear magnetism, i.e. the effect of the spatial com ponents of the vector fields is examined, and the difference between the no nrelativistic and relativistic RPA predictions for the nuclear matter compr ession modulus is explained. (C) 2001 Elsevier Science B.V. All rights rese rved.