Collective excitations and energy-weighted sum rules in relativistic random phase approximation with vacuum polarization

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.