  The tensor-force effects on the evolution of the spin-orbit splittings in the
neutron drops are investigated within the framework of the relativistic
Hartree-Fock theory. For fair comparisons on the pure mean-field level, the
results of the relativistic Brueckner-Hartree-Fock calculation with the Bonn A
interaction are adopted as meta-data. Through a quantitative analysis, we
certify that the $\pi$-pseudovector ($\pi$-PV) coupling affects the
evolutionary trend through the tensor force embedded. The strength of the
tensor force is explored by enlarging the strength $f_{\pi}$ of the $\pi$-PV
coupling. It is found that weakening the density dependence of $f_{\pi}$ is
slightly better than enlarging it with a factor. We thus provide a
semiquantitative support for the \textit{renormalization persistency} of the
tensor force within the framework of density functional theory. This will serve
as an important guidance for the further development of the relativistic
effective interactions with particular focus on the tensor force.
