Study of the neutron drip line of the $Z=9-11$ isotopic chains

Inspired by the recent experimental breakthrough in identifying the last bound neutron-rich nuclei in the fluorine and neon isotopes, we perform a theoretical study of the $Z=9,10,11,12$ isotopes in the relativistic mean field model. The mean field parameters are those of the PK1 parameterization while 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 correctly reproducing the experimental results of the fluorine and neon isotopes. In addition, we predict $^{39}$Na and $^{40}$Mg to be the last bound neutron-rich nuclei in the sodium and magnesium isotopes.