Isotopic shift and search of magic number in the superheavy region

TL;DR

This study investigates isotopic shifts and potential magic numbers in superheavy nuclei using advanced relativistic models, revealing shell closures at known and predicted neutron numbers, and analyzing their structural and surface properties.

Contribution

It provides a systematic analysis of isotopic shifts and shell closures in superheavy nuclei using multiple relativistic models, including predictions for new magic numbers.

Findings

Shell closures at N=20, 28, 50, 82, 126 confirmed.

Predicted new magic numbers at N=40 and 184 for superheavy nuclei.

Correlation between occupation probabilities and nuclear magicity observed.

Abstract

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.