The existence of bubble nuclei identified by the central depletion in nucleonic density is studied for the conventional magic N (Z) = 8, 20, 28, 40, 50, 82, 126 isotones (isotopes) and recently speculated magic N = 164, 184, 228 superheavy isotones. Many new bubble nuclei are predicted in all regions. Study of density profiles, form factor, single particle levels and depletion fraction (DF) across the periodic chart reveals that the central depletion is correlated to shell structure and occurs due to unoccupancy in s-orbit (2s, 3s, 4s) and inversion of (2s, 1d) and (3s, 1h) states in nuclei upto Z ≤ 82. Bubble effect in superheavy region is a signature of the interplay between the Coulomb and nn-interaction and depletion fraction (DF) is found to increase with Z (Coulomb repulsion) and decrease with isospin. Our results are consistent with the available data. The occupancy in s-state in 34 Si increases with temperature which appears to quench the bubble effect.

Two-proton radioactivity with 2p halo is reported theoretically in light mass nuclei A = 18-34. We predict 19 Mg, 22 Si, 26 S, 30 Ar and 34 Ca as promising candidates of ground state 2p-radioactivity with S 2p < 0 and S p > 0. Observation of extended tail of spatial charge density distribution, larger charge radius and study of proton single particle states, Fermi energy and the wave functions indicate 2p halo like structure which supports direct 2p emission. The Coulomb and centrifugal barriers in experimentally identified 2p unbound 22 Si show a quasi-bound state that ensures enough life time for such experimental probes. Our predictions are in good accord with experimental and other theoretical data available so far.

We employ the relativistic mean-field plus BCS (RMF+BCS) approach to study the behavior of [Formula: see text]-shell by investigating in detail the single particle energies, and proton and neutron density profiles along with the deformations and radii of even–even nuclei. Emergence of new shell closure, weakly bound structure and most recent phenomenon of bubble structure are reported in the [Formula: see text]-shell. [Formula: see text]C, [Formula: see text]O and [Formula: see text]S are found to have a weakly bound structure due to particle occupancy in 2[Formula: see text] state. On the other hand [Formula: see text]O, [Formula: see text]Ca and [Formula: see text]Si are found with depleted central density due to the unoccupied 2[Formula: see text] state and hence they are the potential candidates of bubble structure. [Formula: see text]C and [Formula: see text]O emerge as doubly magic with [Formula: see text] in accord with the recent experiments and [Formula: see text]S emerges as a new proton magic nucleus with [Formula: see text]. [Formula: see text] and [Formula: see text] are predicted as magic numbers in doubly magic [Formula: see text]O, [Formula: see text]Ca and [Formula: see text]Si, respectively. These results are found in agreement with the recent experiments and have consistent with the other parameters of RMF and other theories.

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A fully systematic study of even and odd isotopes (281 ≤ A ≤ 380) of Z = 121 superheavy nuclei is presented in theoretical frameworks of Relativistic mean-field plus state dependent BCS approach and Macroscopic-Microscopic approach with triaxially deformed Nilson Strutinsky prescription. The ground state properties namely shell correction, binding energy, two-and one-proton and neutron separation energy, shape, deformation, density profile and the radius are estimated that show strong evidences for magicity in N = 164, 228. Central depletion in the charge density due to large repulsive Coulomb field indicating bubble like structure is reported. A comprehensive analysis for the possible decay modes specifically α-decay and spontaneous fission (SF) is presented and the probable α-decay chains are evaluated. Results are compared with FRDM calculations and the available experimental data which show excellent agreement.

Transfermium nuclei (101≤Z≤110) are investigated thoroughly to describe structural properties viz. deformation, radii, shapes, magicity, etc. as well as their probable decay chains. These properties are explored using relativistic mean-field (RMF) approach and compared with other theories along with available experimental data. Neutron numbers N=152 and 162 have come forth with a deformed shell gap whereas N=184 is ensured as a spherical magic number. The region with N>168 bears witness of the phenomenon of shape transition and shape coexistence for all the considered isotopic chains. Experimental α-decay half-lives are compared with our theoretical halflives obtained by using various empirical/semi-empirical formulas. The recent formula proposed by Manjunatha et al., which results best among the considered 10 formulas, is further modified by adding asymmetry dependent terms (I and I 2). This modified Manjunatha formula is utilized to predict probable α-decay chains that are found in excellent agreement with available experimental data.

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