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

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 $\pi 2s_{1/2}$ than $\pi 1d_{3/2}$. 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 $\pi 2s_{1/2}$ and $\pi 1d_{5/2}$ 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.

Comments: 5 figures, 2 tables, and 9 pages