The square-well potential is defined by for and for , where is the radius of the well.

The Woods–Saxon potential is given by , where:

is the well depth; is the thickness, the distance over which the potential changes from 10% to 90%; is the radial distance between nuclei; is the atomic mass number; is the radius of the nucleus, calculated using ; is taken to be 1.25 femtometers.

This Demonstration shows the dependence of these potentials on atomic mass, potential well depth, and thickness. The square-well potential graph is colored red and the Woods–Saxon potential graph is colored blue.

Either of these potentials can be used in the Schrödinger equation for the nucleons to predict the distribution of nuclear energy levels. The most striking result is the appearance of magic numbers that enumerate the most stable shells of protons and neutrons.