  We calculated antibaryon ($\bar{B}$ = $\bar{p}$, $\bar{\Lambda}$,
$\bar{\Sigma}$, $\bar{\Xi}$) bound states in selected nuclei within the
relativistic mean-field (RMF) model. The G-parity motivated $\bar{B}$-meson
coupling constants were scaled to yield corresponding potentials consistent
with available experimental data. Large polarization of the nuclear core caused
by $\bar{B}$ was confirmed. The $\bar{p}$ annihilation in the nuclear medium
was incorporated by including a phenomenological imaginary part of the optical
potential. The calculations using a complex $\bar{p}$-nucleus potential were
performed fully self-consistently. The $\bar{p}$ widths significantly decrease
when the phase space reduction is considered for $\bar{p}$ annihilation
products, but they still remain sizeable for potentials consistent with
$\bar{p}$-atom data.
