The Oxygen core inside the Magnesium isotopes

We have studied the ground state bulk properties of magnesium isotopes using axially symmetric relativistic mean field formalism. The BCS pairing approach is employed to take care of the pairing correlation for the open shell nuclei. The contour plot of the nucleons distribution are analyzed at various parts of the nucleus, where clusters are located. The presence of an $^{16}$O core along bubble like $\alpha$-particle(s) and few {\it nucleons} are found in the Mg isotopes.