Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Central depressions in the charge density profiles of the nuclei around
  $^{46}$Ar   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.

33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an