Abstract: Inspired by the recent experiments [1]-[3] indicating
unusual doubly magic nucleus 24O which lies just at the neutron
drip-line and encouraged by the success of our relativistic mean-field
(RMF) plus state dependent BCS approach for the description of
the ground state properties of the drip-line nuclei [23]-[27], we have
further employed this approach, across the entire periodic table, to
explore the unusual shell closures in exotic nuclei. In our RMF+BCS
approach the single particle continuum corresponding to the RMF is
replaced by a set of discrete positive energy states for the calculations
of pairing energy. Detailed analysis of the single particle spectrum,
pairing energies and densities of the nuclei predict the unusual proton
shell closures at Z = 6, 14, 16, 34, and unusual neutron shell closures
at N = 6, 14, 16, 34, 40, 70, 112.