  The neutron skin in deformed nuclei is generally not uniformly distributed
but has an angular distribution, depending on both the spin-dependent nuclear
interaction and the nuclear symmetry energy. To extract the information of the
deformed neutron skin, we have explored the possibility of using free spectator
nucleons in central tip-tip and body-body collisions at top RHIC energy with
four typical deformed nuclei. The density distributions of neutrons and protons
are consistently obtained from the Skyrme-Hartree-Fock-Bogolyubov calculation,
and the angular distribution of the neutron skin can be varied by adjusting the
strength of the nuclear spin-orbit coupling. With the information of spectator
nucleons obtained based on a Monte-Carlo Glauber model, the free spectator
nucleons are generated from a multifragmentation process. By investigating the
results from different systems and with different collision configurations, we
found that although it is difficult to probe the deformed neutron skin in
$^{96}$Zr and $^{238}$U by their collisions, it is promising to extract the
polar angular distributions of the neutron skin in $^{96}$Ru and $^{197}$Au by
comparing the yield ratios of free spectator neutrons to protons in their
central tip-tip and body-body collisions. The proposed observables can be
measured by dedicated zero-degree calorimeters in heavy-ion collision
experiments that have been carried out in recent years by RHIC.
