Inspired by the recent debate as to whether the proton drip-line nucleus ${}^{22}\mathrm{Al}$ demonstrates a halo structure in its ground state, we have analyzed theoretical results for ${}^{22}\mathrm{Al}$ and a number of neighboring nuclei especially along isotopic, isotonic, and isobaric chains. Two state-of-the-art nuclear models, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) and its extension in triaxial deformation (TRHBc), are used, where the effects of pairing, deformation, and the continuum are included self-consistently. Although the valence proton of the ${}^{22}\mathrm{Al}$ nucleus is found very loosely bound, in concordance with experimental data, its spatial distribution is found to hardly penetrate the potential barrier. Its wave function is found to consist predominately of $\ell =2$ components, for which halo formation is disfavored. Comparisons with results for isobars reveal a somewhat more extended density distribution than those of the stable or neutron-rich counterparts, but comparisons along isotopic, isotonic, and isobaric chains reveal no discontinuities in size evolution, which, if present, might have signaled exotic structures. The combined theoretical analysis of spatial distributions and binding employed in this work can be applied to explore other proton-halo candidates and their neighbors as proton drip-line nuclei become more and more accessible experimentally for detailed studies.

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• Nuclear structure & decays
• Nucleon distribution
• Rare & new isotopes
• 20 ≤ A ≤ 38
• Nuclear density functional theory