  By using a phenomenologically successful Woods-Saxon potential, I study the
shape and shell structure of (A) neutron drip line nuclei with 10 \leq N \leq
60, (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 a
representative of so-called N=40 "island of inversion (IoI)" nuclei. First, the
shell structure that is unique in very weakly-bound neutrons is systematically
studied, 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 the
shell structure in r-process nuclei from that in stable nuclei is examined.
Third, the similarity and the difference between the shell structure of N=20
IoI nuclei and that of N=40 IoI nuclei are analyzed. As a result of it, it is
concluded that in Fe and Cr isotopes the deformation called "N=40 IoI"
continuing up to N=50 is unlikely.
