The Woods-Saxon potential is a mean field potential for the nucleons (protons and neutrons) inside an atomic nucleus. It represent an average potential that a given nucleon feels from the forces applied on each nucleon. The parametrization is $$\hat{u}_{\mathrm{ext}}(r)=-\frac{V_0}{1+\exp{(r-R)/a}},$$ with $V_0\approx 50$ MeV representing the potential well depth, $a\approx 0.5$ fm length representing the "surface thickness" of the nucleus and $R=r_0A^{1/3}$, with $r_0=1.25$ fm and $A$ the number of nucleons. The value for $r_0$ can be extracted from a fit to data, see for example M. Kirson's article.