  The isoscalar and isovector collective multipole excitations in stable nuclei
are studied in the framework of relativistic random-phase approximation with
the vacuum polarization arising from the nucleon-antinucleon field. A fully
self-consistent calculation which guarantees the decoupling of the spurious
state and the conservation of the multipole-transition current is carried out
by using the derivative-expansion method for the description of the vacuum
contribution. A remarkable effect of the inclusion of the vacuum polarization
is the increase of the effective mass, $m^*/m_N \sim 0.8$; for all multipole
modes, the energy-weighted sum rule values with the vacuum polarization are
smaller than those of the relativistic model without the vacuum polarization,
which typically has the effective mass $m^*/m_N \sim 0.6$. Also, the present
model can give an excellent agreement with experimental data on the excitation
energy, in particular, for the isoscalar quadrupole resonances in which it was
previously reported that the calculated energies in the relativistic model are
about 1-2 MeV above the experimental values. It is shown, further, that the
change of the shell structure due to the inclusion of the vacuum polarization
plays an important role in the improvement of the discrepancies seen in the
dipole compression modes. On the other hand, the isoscalar monopole resonance
has a similar peak whether or not the vacuum polarization is taken into
account, if the compression modulus is kept the same in the analysis.
