With the binding energies and configurations determined experimentally, the root-mean-square radii are calculated for a number of single-particle states by numerically solving the Sch{o}rdinger equations. By studying the relations between the radii and separation energies, the new scaling laws and necessary conditions for neutron halos and proton halos are established, respectively. Especially the existence region of true proton halos is pointed out. It is found that the effects of short-distance behaviours of valence nucleons at the edges of interaction potentials can not be disregarded. Moreover, by means of the radii of interaction potentials, the contributions of outer parts are estimated as the criterions of halos.
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