  Using the density matrix renormalization group technique, we calculate
numerically the low energy excitation spectrum and magnetization curve of the
spin-1 antiferromagnetic chain in a staggered magnetic field, which is expected
to describe the physics of $R_2 Ba Ni O_5 (R \neq Y) $ family below the N\'eel
temperature of the magnetic rare-earth ($R$) sublattice. These results are
valid in the entire range of the staggered field, and agree with those given by
the non-linear $\sigma$ model study for small fields, but differ from the
latter for large fields. They are consistent with the available experimental
data. The correlation functions for this model are also calculated. The
transverse correlations display the anticipated exponential decay with shorter
correlation length, while the longitudinal correlations show explicitly the
induced staggered magnetization.
