  The quantum vacuum in a many-body system of finite nuclei has been
investigated within the relativistic Hartree approach which describes the bound
states of nucleons and anti-nucleons consistently. The contributions of the
Dirac sea to the source terms of the meson-field equations are taken into
account up to the one-nucleon loop and one-meson loop. The tensor couplings for
the $\omega$- and $\rho$-meson are included in the model. After adjusting the
parameters of the model to the properties of spherical nuclei, a large
effective nucleon mass $m^{*}/M_{N} \approx 0.78$ is obtained. The overall
nucleon spectra of shell-model states are in agreement with the data. The
computed anti-nucleon spectra in the vacuum differ about 20 -- 30 MeV with and
without the tensor-coupling effects.
