Relativistic Hartree approach with exact treatment of vacuum polarization for finite nuclei

We study the relativistic Hartree approach with an exact treatment of the vacuum polarization in the Walecka (σ-ω) model. The contribution from the vacuum polarization of the nucleon-antinucleon field to the source term of the meson fields is evaluated by performing the energy integrals of the Dirac Green function along the imaginary axis. With the present method of calculating the vacuum polarization in finite system, the total binding energies and charge radii of ¹⁶O and ⁴⁰Ca can be reproduced. On the other hand, the level splittings in the single-particle level, in particular the spin-orbit splittings, are not described well because the inclusion of vacuum effect provides a large effective mass with small meson fields. We also show that the derivative expansion of the effective action is fairly useful for the estimation of the vacuum effect.