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 usual particle-hole states, but also
a-h 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 116Sn. It is shown that,
because the matrix elements of the time-like component of the vector meson
fields which couple the a-h configurations with the ph-configurations 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.Comment: 21 pages,2 figures, Nucl.Phys.A in pres
