  Possible deformation of odd-N nuclei with N $\approx$ 28 towards the neutron
drip line is investigated using the Nilsson diagram based on deformed
Woods-Saxon potentials. Both weakly-bound and resonant one-particle levels are
properly obtained by directly solving the Schr\"{o}dinger equation in mesh of
space coordinate with the correct boundary condition. If we use the same
diffuseness of the potential as that of $\beta$-stable nuclei, the energy
difference between the neutron 2p$_{3/2}$ and 1f$_{7/2}$ levels becomes very
small or the N=28 energy gap almost disappears, as the binding energies of
those levels approach zero. This suggests that the ground states of those
neutron drip line nuclei are likely to be deformed. In particular, the
spin-parity and the magnetic moment of the ground state of odd-N nuclei,
$^{43}_{16}$S$_{27}$ and $^{45}_{16}$S$_{29}$, are examined. Moreover, it is
suggested that in $^{39}_{12}$Mg$_{27}$ lying outside the drip line the lowest
resonant state may have 5/2$^{-}$, if the N=28 energy gap almost vanishes.

Nuclear Theory