  A recent experimental breakthrough identified the last bound neutron-rich
nuclei in fluorine and neon isotopes. Based on this finding, we perform a
theoretical study of $Z=9, 10, 11, 12$ isotopes in the relativistic mean field
(RMF) model. The mean field parameters are assumed from the PK1
parameterization, and the pairing correlation is described by the particle
number conservation BCS (FBCS) method recently formulated in the RMF model. We
show that the FBCS approach plays an essential role in reproducing experimental
results of fluorine and neon isotopes. Furthermore, we predict $^{39}$Na and
$^{40}$Mg to be the last bound neutron-rich nuclei in sodium and magnesium
isotopes.
