  The relativistic Hartree approach describing the bound states of both
nucleons and anti-nucleons in finite nuclei has been extended to include tensor
couplings for the $\omega$- and $\rho$-meson. After readjusting the parameters
of the model to the properties of spherical nuclei, the effect of
tensor-coupling terms rises the spin-orbit force by a factor of 2, while a
large effective nucleon mass $m^{*}/M_{N} \approx 0.8$ sustains. The overall
nucleon spectra of shell-model states are improved evidently. The predicted
anti-nucleon spectra in the vacuum are deepened about 20 -- 30 MeV.
