Narrow Results

We employ the relativistic mean-field plus BCS (RMF+BCS) approach to study the behavior of $sd$-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 $sd$-shell. ${}^{22}$C, ${}^{24}$O and ${}^{26}$S are found to have a weakly bound structure due to particle occupancy in 2$s_{1/2}$ state. On the other hand ${}^{22}$O, ${}^{34}$Ca and ${}^{34,48}$Si are found with depleted central density due to the unoccupied 2$s_{1/2}$ state and hence they are the potential candidates of bubble structure. ${}^{22}$C and ${}^{24}$O emerge as doubly magic with $N=16$ in accord with the recent experiments and ${}^{26}$S emerges as a new proton magic nucleus with $Z=16$. $N=14$ and $Z=14$ are predicted as magic numbers in doubly magic ${}^{22}$O, ${}^{34}$Ca and ${}^{34,48}$Si, respectively. These results are found in agreement with the recent experiments and have consistent with the other parameters of RMF and other theories.

We present a systematic description of the exotic features in the ground states of light nuclei from the stable valley to the drip lines. A study with the even and odd isotopes of Ne, Mg, Si, S and Ar has been performed using theoretical formalisms (i) Relativistic mean-field plus state-dependent BCS approach and (ii) Macroscopic–Microscopic (MM) approach using the triaxially deformed Nilsson–Strutinsky Method. The computed binding energies and one- and two-neutron separation energies using both the theories show magic character of $N=14,20,28$ and 40. The neutron and proton radii and the neutron densities show a well-developed neutron skin in the neutron-rich isotopes. The exotic phenomena such as weakly bound structures and the central density depletion characterized as bubble effect are explored. Our calculations for the single particle levels, density profiles and the charge form factors indicate bubble-like structures. Few new candidates of bubble nuclei are identified. Most of the nuclei in this region are found deformed with mostly prolate shape and few triaxial shapes while many nuclei exhibit the phenomenon of shape coexistence. Our results display a reasonable agreement between both the theories and the available experimental data.

In this work, we identify a unique and novel feature of central density depletion in both proton and neutron named as doubly bubble nuclei in $50\le Z(N)\le 82$ region. The major role of 2d-3s single-particle (s.p.) states in the existence of halo and bubble nuclei is probed. The occupancy in s.p. state 3s${}_{1/2}$ leads to the extended neutron density distribution or halo while the unoccupancy results in the central density depletion. By employing the Relativistic Mean-Field (RMF) approach along with NL3* parameter, the separation energies, s.p. energies, pairing energies, proton and neutron density profiles along with deformations of even–even nuclei are investigated. Our results are concise with few other theories and available experimental data. Emergence on new shell closure and the magicity of conventional shell closures are explored systematically in this yet unknown region.

The charge, proton and neutron density distributions along with nuclear properties were calculated by Hartree–Fock approach with Skyrme force interaction for isotopic Pb chain ($88\le N\le 184$). The effects of correlation on neutron skin thicknesses by obtaining bulk and surface contributions were analyzed by three different approaches. The occurrence of the nuclei with bubble structure due to central depletion in nucleonic was investigated for Pb isotopes as a function of relative neutron excess $I=(N-Z)/A$. The important role of the bubble effect in heavy region was explained by the relation between Coulomb and nn-interaction. The single particle energy levels were determined by each $j=l\mp \frac{1}{2}$ state of stable Pb isotopes, as well as charge form factors $F_{\mathrm{\text{ch}}}(k)$. Besides, the average neutron–proton ${\delta V}_{\mathrm{\text{np}}}$ and residual neutron–proton ${\delta }_{\mathrm{\text{np}}}$ interactions of the Pb isotopes were calculated by the theoretical binding energies. The fluctuations in the obtained results were considered in detail because its variation may give a good criterion for the mass model approaches.

The systematic search of axial ground state and the emergence of new gaps in neutron-rich ${}^{44-52}$Ar isotopes are the challenging of current calculations of relativistic and nonrelativistic mean field models. For this purpose, we have employed the model based on Relativistic Hartree–Bogoliubov (RHB) with the density-dependent effective interaction of point coupling DD-PCX type. However, the nonrelativistic mean field calculations based on Hartree-Fock model were carried out with Skyrme SV-min parametrization. All the present calculations were performed within axial symmetries. The results provide that most of isotopes show an oblate-deformed ground state. In particular, ${}^{50}$Ar and ${}^{52}$Ar display a spherical shape in their ground states with SV-Min calculations. There is a notable signature of the sub-shell closure at neutron number $N=32$, whereas $N=34$ is expected to be nearly quenched in the spherical ground. Furthermore, coexistence features are predicted in the neutron-rich ${}^{44}$Ar isotope. We have also studied the neutron axial densities and its central depletion in the well-deformed grounds for the first time. In addition to these, the proton single-particle evolution and bubble-like structure at ${}^{46}$Ar are very well reproduced with DD-PCX calculations.

The proton density distribution of ⁴⁶Ar is calculated in the framework of the Skyrme-Hartree-Fock (SHF) approach with the SLy5, SLy5+T and SLy5+T_w interactions. It is shown that the tensor force in the SLy5+T_w interaction favors its bubble structure due to the inversion between the single-proton states 2s_1/2 and 1d_3/2. However, the SLy5+T interaction can not lead to any 2s_1/2-1d_3/2 inversion, consequently no bubble structure can be found. In addition, a detailed discussion on the competition between tensor force and pairing correlation on the bubble formation is performed within the Skyrme-Hartree-Fock-Bogoliubov (SHFB) approach.