  The ground state bulk properties such as binding energy, root-mean-square
radius, pairing energy, nuclear density distributions, and single-particle
energies are calculated for the isotopic chain of Ca, Sn, Pb, and Z = 120
nuclei. The relativistic mean-field with recently developed G3, IOPB-1, and
Relativistic-Hartree-Bogoliubov with density-dependent DD-ME1 and DD-ME2
parameter sets are used in the present analysis. The respective shifts over the
isotopic chain for the structural observables and surface property like
symmetry energy are also estimated using a three-point method, which is crucial
for the systematic analysis of the shell/sub-shell closure. The calculated
results are compared with the available experimental data for various bulk
properties, wherever available. A multiple isotopic shifts leads to the
shell/sub-shell closure at N = (20 \& 28), (50 \& 82), and 126 for Ca, Sn, and
Pb isotopes, respectively, are observed. The analysis also supports the neutron
magic at N = 40 and 184 for highly neutron-rich $^{60}$Ca, and $^{304}$120,
predicted to be the next double magic beyond $^{208}$Pb, respectively.
Observing the occupancy number, we notice the higher neutron orbitals are
mostly occupied before the lower one, which causes the kinks at neutron magic
with an amalgam in the isotopic chain trend above nuclei. We also notice the
correlation between the occupation probabilities and the magicity of a nucleus
and vice-versa.
