  We perform a systematic study of all the traditional neutron magic nuclei
with $N$ = 8, 20, 28, 50, 82, and 126, from the neutron drip line to the proton
drip line. We adopt the deformed relativistic mean field (RMF) theory as our
framework and treat pairing correlations by a simple BCS method with a
zero-range $\delta$-force. Remarkable agreement with the available experimental
data is obtained for the binding energies, the two- and one-proton separation
energies, and the nuclear charge radii. The calculated nuclear deformations are
compared with the available experimental data and the predictions of the FRDM
mass formula and the HFBCS-1 mass formula. We discuss, in particular, the
appearance of sub-shell magic nuclei by observing irregular behavior in the
two- and one-proton separation energies.
