Isospin dependence of shell closure at N = 90 and 92 for medium mass nuclei using relativistic energy density functional

Abstract

In a recent study [Europhys. Lett. 146, (2024), 14001], a novel relativistic parameterisation of the energy density functional (EDF) at local density was integrated into the coherent density fluctuation model (CDFM). This approach employed the density-dependent DD-ME2 parameter within the relativistic Hartree-Bogoliubov framework, alongside the well-established non-linear NL3 force parameter, to investigate the surface properties of a few doubly-magic nuclei. In the present work, we extend this new relativistic EDF formulation to a much broader region: the evolution of shell structure across several open- and closed-shell nuclei of intermediate-mass isotopic chains, specifically Kr ($Z=36$), Sr ($Z=38$), Te ($Z=52$), Xe ($Z=54$), Ba ($Z=56$), Ce ($Z=58$), Nd ($Z=60$) and Sm ($Z=62$). Using the CDFM formalism, we translate key nuclear matter quantities, such as the symmetry energy and its derivatives, from momentum space to coordinate space at local densities. This procedure is particularly relevant when investigating nuclei near the drip lines. Our findings demonstrate that the symmetry energy successfully reproduces the conventional magic numbers $N=50$ and 82 while indicating the emergence of new shell and/or sub-shell closures around $N=90$ and 92. Furthermore, we decompose the symmetry energy into its volume and surface components, using two approaches, and perform an extensive comparison to assess their impact on the identification of shell closures. We also examine how neutron-proton asymmetry influences the symmetry energy along these isotopic chains. In general, this study highlights novel regions of interest in the medium-mass region of the nuclear chart. It emphasises the need for experimental investigations of the newly suggested shell closures.