Microscopic description of the proton halo in $^{12}$N

The year 2025 marks the 40th anniversary of the discovery of halo nuclei and the 15th anniversary of the development of the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). In this work, we present the first DRHBc description of the proton halo phenomenon. The available experimental proton separation energies and empirical matter root-mean-square (rms) radii are reasonably well reproduced for the $N=5$ isotones, ranging from the stable nucleus $^{9}$Be to the drip-line nucleus $^{12}$N. In particular, the DRHBc theory captures the abrupt increase in rms radii at $^{12}$N, unambiguously corroborating its proton halo structure. The formation of this halo is attributed to the occupation of a weakly bound orbital with dominant $1p$ components by the valence proton, which contributes approximately $90\%$ to the diffused proton density of $^{12}$N at large distances from the nuclear center. A shape decoupling between the prolate core and the oblate halo in $^{12}$N is predicted.