  Within an isospin- and momentum-dependent transport model IBUU11 using as an
input nucleon density profiles from Hartree-Fock calculations based on a
modified Skyrme-like (MSL) model, we study the influence of the uncertainty of
the neutron skin thickness on the $\pi^{-}/\pi^{+}$ ratio in both central and
peripheral Pb+Pb collisions at beam energies of 400 MeV/nucleon and 1000
MeV/nucleon. Within the current experimental uncertainty range of neutron skin
in $^{208}$Pb, while the neutron skin effect on the \rpi ratio is negligible in
central reactions at both energies, it increases gradually with increasing
impact parameter and becomes comparable with or even larger than the symmetry
energy effect in peripheral collisions especially at 400 MeV/nucleon. Moreover,
we found that while the \rpi ratio is larger with a softer \esym in central
collisions, above certain impact parameters depending on the size of the
neutron skin, a stiffer \esym can lead to a larger \rpi ratio as most of the
pions are produced at densities below the saturation density in these
peripheral reactions. Thus, a clear impact parameter selection is important to
extract reliable information about the \esym at suprasaturation densities (size
of neutron skin) from the $\pi^-/\pi^+$ ratio in central (peripheral) heavy-ion
collisions.
