LAUSR

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.