Scaling laws of valence nucleon distributions for single-particle states

Abstract

Under the single-particle potential model, the root-mean-square radii for a number of single-particle states have been calculated by numerically solving the Schr\"odinger equations, with the binding energies and configurations determined experimentally. By studying the relations between the radii and the separation energies, the scaling laws of valence nucleon distributions for these single-particle states are obtained. In the light of these scaling laws, the necessary conditions for neutron halos and proton halos are, respectively, deduced. The existence region of proton halos is pointed out. It is found that the behavior of valence nucleons around the radii of interaction potentials could not be disregarded.