  (Abridged) Aims: We study the effects related to departures from non-local
thermodynamic equilibrium (NLTE) and homogeneity in the atmospheres of red
giant stars in Galactic globular cluster NGC 6752, to assess their influence on
the formation of Ba II lines. Methods: One-dimensional (1D) local thermodynamic
equilibrium (LTE) and 1D NLTE barium abundances were derived using classical 1D
ATLAS stellar model atmospheres. The three-dimensional (3D) LTE abundances were
obtained for 8 red giants on the lower RGB, by adjusting their 1D LTE
abundances using 3D-1D abundance corrections, i.e., the differences between the
abundances obtained from the same spectral line using the 3D hydrodynamical
(CO5BOLD) and classical 1D (LHD) stellar model atmospheres. Results: The mean
1D barium-to-iron abundance ratios derived for 20 giants are <[Ba/Fe]>_{1D
NLTE} = 0.05 \pm0.06 (stat.) \pm0.08 (sys.). The 3D-1D abundance correction
obtained for 8 giants is small (~+0.05 dex), thus leads to only minor
adjustment when applied to the mean 1D NLTE barium-to-iron abundance ratio for
the 20 giants, <[Ba/Fe]>_{3D+NLTE} = 0.10 \pm0.06(stat.) \pm0.10(sys.). The
intrinsic abundance spread between the individual cluster stars is small and
can be explained in terms of uncertainties in the abundance determinations.
Conclusions: Deviations from LTE play an important role in the formation of
barium lines in the atmospheres of red giants studied here. The role of 3D
hydrodynamical effects should not be dismissed either, even if the obtained
3D-1D abundance corrections are small. This result is a consequence of subtle
fine-tuning of individual contributions from horizontal temperature
fluctuations and differences between the average temperature profiles in the 3D
and 1D model atmospheres: owing to the comparable size and opposite sign, their
contributions nearly cancel each other.
