Effects of pairing, continuum, and deformation on particles in the classically forbidden regions for Mg isotopes

Particles in the classically forbidden regions are studied based on the deformed relativistic Hartree-Bogoliubov theory in continuum with PC-PK1 for magnesium isotopes. By analyzing the neutron and proton radii, it is found that the largest deviations from the empirical values appear at the predicted neutron halo nuclei $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$. Consistently, notable increases at $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$ are found in the total number of neutrons in the classically forbidden regions, which includes the number of neutrons in continuum. It is shown that the deformation effect, in general, increases the number of particles in the classically forbidden regions below the continuum threshold. The most deeply bound single-particle states play the dominant roles in the increase caused by deformation.