  The shell evolution has been studied extensively within the framework of
interacting shell model, while the studies from the single particle viewpoint
is relatively lacking or neglected. In particular, the isospin dependence of
spin-orbit splitting has become increasingly important as $N/Z$ increases in
neutron-rich nuclei. Following the initial independent-particle strategy
towards explaining the occurrence of magic numbers, we have systematically
investigated the isospin effect on the shell evolution of neutron-rich nuclei
within the Woods-Saxon (WS) mean-field potential plus the spin-orbit term. It
is found that new magic numbers $N = 14$ and $N =16$ may emerge in neutron-rich
nuclei if one changes the sign of the isospin-dependent term in the spin-orbit
coupling while the traditional magic number $N = 20$ may disappear. The magic
number $N = 28$ is expected to be destroyed despite the sign choice of the
isospin part in spin-orbit splitting, while $N = 50$ may disappear and $N = 82$
persists within the single particle scheme. Besides, an appreciable amount of
energy gap appears at $N = 32$ and 34 in neutron-rich Ca isotopes. All these
results are more consistent with those of the interacting shell model, when the
sign of the isospin term of the WS potential is different from that of the
corresponding spin-orbit coupling part. The present study may provide a more
reasonable starting point for not only the interacting shell but also other
nuclear many-body calculations towards the neutron-dripline.
