Neutron shell structure and the resulting possible deformation in the neighborhood of neutron-drip-line nuclei are systematically discussed, based on both bound and resonant neutron one-particle energies obtained from spherical and deformed Woods-Saxon potentials. Owing to the unique behavior of weakly bound and resonant neutron one-particle levels with smaller orbital angular momenta l, a systematic change in the shell structure and thereby a change in the neutron magic numbers are pointed out, compared with those of stable nuclei expected from the conventional j-j shell model. For a spherical shape with the operator of the spin-orbit potential conventionally used, the l(j) levels belonging to a given oscillator major shell with parallel spin and orbital angular momenta tend to gather together in the energetically lower half of the major shell, while the levels with antiparallel spin and orbital angular momenta gather in the upper half. This tendency leads to a unique shell structure and possible deformation when neutrons start to occupy the orbits in the lower half of the major shell. Among others, the neutron magic number N = 28 disappears and N = 50 may disappear, while the magic number N = 82 may presumably survive owing to the large l = 5 spin-orbit splitting for the 1h(11/2) orbit. On the other hand, an appreciable amount of energy gap may appear at N = 16 and 40 for spherical shape, while neutron-drip-line nuclei in the region of neutron numbers above N = 20, 40, and 82, namely, N approximate to 21-28, N approximate to 41-54, and N approximate to 83-90, may be quadrupole deformed, although the possible deformation also depends on the proton number of the respective nuclei.
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