Central depressions in the charge density profiles of the nuclei around $^{46}$Ar

TL;DR

This study investigates proton bubble-like structures in argon isotopes and N=28 isotones using relativistic mean-field theories, finding no bubble in argon but predicting bubbles in $^{42}$Si and $^{40}$Mg.

Contribution

It provides the first detailed theoretical analysis of proton bubble structures in these nuclei using RHFB and RHB models, identifying $^{42}$Si as a potential bubble nucleus.

Findings

No proton bubble in argon isotopes due to deep bound proton orbit.

Proton bubble structures predicted in $^{42}$Si and $^{40}$Mg.

$^{42}$Si proposed as a candidate for proton bubble nucleus.

Abstract

The occurrence of the proton bubble-like structure has been studied within the relativistic Hartree-Fock-Bogoliubov (RHFB) and relativistic Hartree-Bogoliubov (RHB) theories by exploring the bulk properties, the charge density profiles and single proton spectra of argon isotopes and $N = 28$ isotones. It is found that the RHFB calculations with PKA1 effective interaction, which can properly reproduce the charge radii of argon isotopes and the $Z=16$ proton shell nearby, do not support the occurrence of the proton bubble-like structure in argon isotopes due to the prediction of deeper bound proton orbit $\pi2s_{1/2}$ than $\pi1d_{3/2}$. For $N = 28$ isotones, $^{42}$Si and $^{40}$Mg are predicted by both RHFB and RHB models to have the proton bubble-like structure, owing to the large gap between the proton $\pi2s_{1/2}$ and $\pi1d_{5/2}$ orbits, namely the $Z=14$ proton shell. Therefore, $^{42}$Si is proposed as the potential candidate of proton bubble nucleus, which has longer life-time than $^{40}$Mg.