Possible deformation of odd-N nuclei with N $\approx$ 28 towards the neutrondrip line is investigated using the Nilsson diagram based on deformedWoods-Saxon potentials. Both weakly-bound and resonant one-particle levels areproperly obtained by directly solving the Schr\"{o}dinger equation in mesh ofspace coordinate with the correct boundary condition. If we use the samediffuseness of the potential as that of $\beta$-stable nuclei, the energydifference between the neutron 2p$_{3/2}$ and 1f$_{7/2}$ levels becomes verysmall or the N=28 energy gap almost disappears, as the binding energies ofthose levels approach zero. This suggests that the ground states of thoseneutron drip line nuclei are likely to be deformed. In particular, thespin-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 issuggested that in $^{39}_{12}$Mg$_{27}$ lying outside the drip line the lowestresonant state may have 5/2$^{-}$, if the N=28 energy gap almost vanishes.
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