  With the PICR hydrodynamic model, we study the polarization splitting between
$\Lambda$ and $\bar{\Lambda}$ at RHIC BES energy range, based on the meson
field mechanism. Our results fit to the experimental data fairly well. Besides,
two unexpected effect emerges: (1) the baryon density gradient has non-trivial
and negative contribution to the polarization splitting; (2) for 7.7 GeV Au+Au
collisions within the centrality range of 20\%-50\%, the polarization splitting
surprisingly increases with the centrality decreases. The second effect might
help to explain the significant signal of polarization splitting measured in
STAR's Au+Au 7.7 Gev collisions.
