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By using a phenomenologically successful Woods-Saxon potential, I study theshape and shell structure of (A) neutron drip line nuclei with 10 \leq N \leq60, (B) neutron-rich nuclei related to the r- process with 40 \leq N \leq 90,and (C) one-particle spectra in the potential provided by the nucleus 70Fe as arepresentative of so-called N=40 "island of inversion (IoI)" nuclei. First, theshell structure that is unique in very weakly-bound neutrons is systematicallystudied, and the approximate neutron number of odd-N nuclei at which spherical(or deformed) halos can be found is pinned down. Second, the difference of theshell structure in r-process nuclei from that in stable nuclei is examined.Third, the similarity and the difference between the shell structure of N=20IoI nuclei and that of N=40 IoI nuclei are analyzed. As a result of it, it isconcluded that in Fe and Cr isotopes the deformation called "N=40 IoI"continuing up to N=50 is unlikely.

Shape and shell-structure of lighter (N<90) neutron-rich nuclei based on phenomenological Woods-Saxon potential