Evolution of $N=20,28,50$ shell closures in the $ 20 \leqslant Z \leqslant 30$ region in deformed relativistic Hartree-Bogoliubov theory in continuum

TL;DR

This study uses advanced relativistic density functional theory to analyze how traditional nuclear shell closures at N=20, 28, and 50 evolve across isotopic chains in the Z=20-30 region, revealing deformation effects that quench some closures.

Contribution

It applies the deformed relativistic Hartree-Bogoliubov theory in continuum with the PC-PK1 functional to systematically study shell evolution in this nuclear region, highlighting deformation-induced quenching of certain shell closures.

Findings

N=50 shell closure quenched in Z=21-27 due to deformation

N=28 shell closure disappears in Mn isotopes due to deformation

N=20 shell closure predicted in some isotopes but inconsistent with data

Abstract

Magicity, or shell closure, plays an important role in our understanding of complex nuclear phenomena. In this work, we employ one of the state-of-the-art density functional theories, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the density functional PC-PK1, to investigate the evolution of the $N=20,28,50$ shell closures in the $ 20 \leqslant Z \leqslant 30$ region. We show how these three conventional shell closures evolve from the proton drip line to the neutron drip line by studying the charge radii, two-neutron separation energies, two-neutron gaps, quadrupole deformations, and single-particle levels. In particular, we find that in the $ 21 \leqslant Z \leqslant 27$ region, the $N=50$ shell closure disappears or becomes quenched, mainly due to the deformation effects. Similarly, both experimental data and theoretical predictions indicate that the $N=28$ shell closure disappears in the Mn isotopic chain, also predominantly due to the deformation effects. The DRHBc theory predicts the existence of the $N=20$ shell closure in the Ca, Sc, and Ti isotopic chains, but the existing data for the Ti isotopes suggests the contrary, and therefore more investigations are needed.