  We study the relativistic Hartree approach with the exact treatment of the
vacuum polarization in the Walecka sigma-omega model. The contribution from the
vacuum polarization of 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 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 nicely 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 which has been used to calculate the vacuum
contribution for finite nuclei gives a fairly good approximation.
