Scaling Law of s-wave Valence Proton Distributions

In the framework of the single-particle potential model, the root-mean-square radii of s-wave valence proton distributions for P and S isotopes have been systematically calculated. The scaling law of s-wave valence proton distributions is obtained by analyzing the relation between radii and separation energies. Necessary condition for the occurrence of 2s1/2-state proton halos is deduced from the scaling law. Quantitative condition derived from this work can to some extent serve as reference for proton halo search.